{"id":498,"date":"2025-11-18T15:20:07","date_gmt":"2025-11-18T14:20:07","guid":{"rendered":"https:\/\/clases.jesussoto.es\/?p=498"},"modified":"2025-11-18T22:18:26","modified_gmt":"2025-11-18T21:18:26","slug":"biomath-integracion-numerica-con-maxima","status":"publish","type":"post","link":"https:\/\/clases.jesussoto.es\/?p=498","title":{"rendered":"MathBio: Integraci\u00f3n num\u00e9rica con maxima"},"content":{"rendered":"<h2>Regla del trapecio<\/h2>\n<p>Muchas veces calcular la primitiva de una funci\u00f3n resulta tremendamente dif\u00edcil, cuando no imposible. En esos casos lo que hacemos en encontrar una aproximaci\u00f3n mediante m\u00e9todos de integraci\u00f3n num\u00e9rica.<\/p>\n<p>La idea es aproximar la integral por trapecios. La m\u00e1s sencilla es la regla del trapecio simple, pero la que se utiliza es la compuesta, pues da una aproximaci\u00f3n mejor. Sea \\(f\\) una funci\u00f3n real definida en \\([a,b]\\), entonces \\[\\int_a^b f(x) dx = \\frac{h}{2} \\left[ f(a) + f(b) + 2\\sum_{k=1}^{n-1} f\\left(a + k h\\right) \\right]-\\frac{(b-a)h^2}{12}f^{(2)}(\\xi),\\, \\xi\\in (a,b)\\]<\/p>\n<blockquote><p><strong>Ejemplo:<\/strong> \u00bfCu\u00e1l es el \u00e1rea aproximada de la funci\u00f3n \\(f(x)=\\frac{\\sin(x^2)}{\\sqrt{x}}\\) en el intervalo \\([1,2]\\)?<\/p><\/blockquote>\n<p><script>\nfunction showHtmlDiv1t23() {\n  var htmlShow1t23 = document.getElementById(\"html-show1t23\");\n  if (htmlShow1t23.style.display === \"none\") {\n    htmlShow1t23.style.display = \"block\";\n  } else {\n    htmlShow1t23.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv1t23()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show1t23\" style=\"display: none;\">\n<!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i3)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">=<\/span><span class=\"code_function\">sin<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">^<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_function\">sqrt<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">a<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_variable\">b<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">2<\/span><span class=\"code_endofline\">$<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[{ }{f}(x){:=}\\frac{{{\\sin{(x)}}^{2}}}{\\sqrt{x}}\\]<\/p>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">Aplicamos la regla del trapecio para n=10<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i6)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">n<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">10<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">b<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_variable\">a<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">Area<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_function\">float<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">a<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">+<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">b<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">+<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_function\">sum<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">a<\/span><span class=\"code_operator\">+<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[{ }0.7542348347388509\\]<\/p>\n<\/div>\n<hr \/>\n<h2>Reglas simples de Simpson<\/h2>\n<h2>Regla simple de Simpson<\/h2>\n<p>\\[\\int_{x_0}^{x_2} f(x) dx =\\frac{h}{3}(f(x_0)+4f(x_1)+f(x_2)) -\\frac{h^5}{90}f^{(4)}(\\xi),\\, \\xi\\in (x_0,x_2) \\] <\/p>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> \u00bfCu\u00e1l es el valor de  \\(\\int_{0}^{\\frac{\\pi}{4}}e^{\\cos x}\\sin x\\ dx\\)?<\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv1q() {\n  var htmlShow1q = document.getElementById(\"html-show1q\");\n  if (htmlShow1q.style.display === \"none\") {\n    htmlShow1q.style.display = \"block\";\n  } else {\n    htmlShow1q.style.display = \"none\";\n  }\n}\n<\/script> <\/p>\n<p><button onclick=\"showHtmlDiv1q()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show1q\" style=\"display: none;\">\n <!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i1)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">=<\/span><span class=\"code_variable\">%e<\/span><span class=\"code_operator\">^<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">cos<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_function\">sin<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }\\operatorname{f}(x)\\operatorname{:=}{{\\% e}^{\\cos{(x)}}} \\sin{(x)}\\]<\/p>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">Utilicemos la regla de Simpson de 1\/3.<br \/>Si partimos de x0=0, tendremos un paso de h:(\u03c0\/4-0)\/2<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i10) <\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">fpprintprec<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">5<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">%pi<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">4<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">0<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">2<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">0<\/span><span class=\"code_operator\">+<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">h<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }\\left[ 0\\operatorname{,}\\frac{{\\pi} }{8}\\operatorname{,}\\frac{{\\pi} }{4}\\right] \\]<\/p>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i12) <\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">S<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">4<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">%<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">numer<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }0.69246\\]<\/p>\n<\/div>\n<hr \/>\n<blockquote>\n<p><strong>Ejercicio:<\/strong> \u00bfCu\u00e1l es el \u00e1rea de la regi\u00f3n entre la curva  \\(y=x^2-x\\) y el eje x desde 0 a 2?<\/p>\n<\/blockquote>\n<p><script>\nfunction showHtmlDiv1() {\n  var htmlShow1 = document.getElementById(\"html-show1\");\n  if (htmlShow1.style.display === \"none\") {\n    htmlShow1.style.display = \"block\";\n  } else {\n    htmlShow1.style.display = \"none\";\n  }\n}\n<\/script> <\/p>\n<p><button onclick=\"showHtmlDiv1()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show1\" style=\"display: none;\">\n<!-- Text cell --><\/p>\n<div class=\"comment\">\n<p>El \u00e1rea encerrada entre la curva y el eje x es la dada en la gr\u00e1fica:<\/p>\n<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i2)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">f<\/span>(<span class=\"code_variable\">x<\/span>)<span class=\"code_operator\">:<\/span><span class=\"code_operator\">=<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">^<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">&#8211;<\/span><span class=\"code_variable\">x<\/span><span class=\"code_endofline\">$<\/span><br \/><span class=\"code_function\">wxdraw2d<\/span>(<span class=\"code_variable\">filled_func<\/span><span class=\"code_operator\">=<\/span><span class=\"code_number\">0<\/span>,<span class=\"code_variable\">fill_color<\/span><span class=\"code_operator\">=<\/span><span class=\"code_variable\">grey<\/span>,<span class=\"code_function\">explicit<\/span>(<span class=\"code_function\">f<\/span>(<span class=\"code_variable\">x<\/span>),<span class=\"code_variable\">x<\/span>,<span class=\"code_number\">0<\/span>,<span class=\"code_number\">2<\/span>),<br \/><span class=\"code_variable\">filled_func<\/span><span class=\"code_operator\">=<\/span>false,<span class=\"code_variable\">color<\/span><span class=\"code_operator\">=<\/span><span class=\"code_variable\">blue<\/span>, <span class=\"code_variable\">line_width<\/span><span class=\"code_operator\">=<\/span><span class=\"code_number\">3<\/span>,<span class=\"code_function\">explicit<\/span>(<span class=\"code_function\">f<\/span>(<span class=\"code_variable\">x<\/span>),<span class=\"code_variable\">x<\/span>,<span class=\"code_number\">0<\/span>,<span class=\"code_number\">2<\/span>),<span class=\"code_variable\">xaxis<\/span><span class=\"code_operator\">=<\/span>true)<span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable><mlabeledtr columnalign=\"right\"><mtd><mtext\/><\/mtd><mtd><mo>0 errores, 0 advertencias<\/mo><\/mtd><\/mlabeledtr><\/mtable><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable><mlabeledtr columnalign=\"left\"><mtd><mtext>(%i2) <\/mtext><\/mtd><mtd\/><\/mlabeledtr><\/mtable><\/math><img decoding=\"async\" src=\"https:\/\/uploads.jesussoto.es\/doc\/Ejer_vol07_2.png\" width=\"598\" style=\"max-width:90%;\" loading=\"lazy\" alt=\" (Gr\u00e1ficos) \"\/><br \/><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable><mlabeledtr columnalign=\"right\"><mtd><mtext>(%o2) <\/mtext><\/mtd><mtd\/><\/mlabeledtr><\/mtable><\/math><!-- Text cell --><\/p>\n<div class=\"comment\">\n<p>Como una parte de la funci\u00f3n es negativa, para calcular el \u00e1rea debemos integrar en dos intervalos [0,1] y [1,2]:<\/p>\n<\/div>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">Utilicemos la regla de Simpson de 1\/3 en cada intervalo.<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i5)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">fpprintprec<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">5<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">0<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">2<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">0<\/span><span class=\"code_operator\">+<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">h<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }\\left[ 0\\operatorname{,}\\frac{1}{2}\\operatorname{,}1\\right] \\]<\/p>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">Recordemos que la funci\u00f3n es negativa, luego cambiamos el signo:<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i6)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">S1<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">4<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">numer<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }0.16666\\]<\/p>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">Para el intervalo [1,2]<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i9)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">h<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">2<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">+<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">h<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">S2<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">4<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">numer<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }\\left[ 1\\operatorname{,}\\frac{3}{2}\\operatorname{,}2\\right] \\]<\/p>\n<p>\\[\\operatorname{ }0.83333\\]<\/p>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">El resultado que buscamos es:<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i10) <\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">S1<\/span><span class=\"code_operator\">+<\/span><span class=\"code_variable\">S2<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }0.99999\\]<\/p>\n<\/div>\n<hr \/>\n<h2>Regla \\(\\frac{3}{8}\\) de Simpson<\/h2>\n<p>\\[\\int_{x_0}^{x_3} f(x) dx =\\frac{3h}{8}(f(x_0)+3f(x_1)+3f(x_2)+f(x_3))-\\frac{3h^5}{80}f^{(4)}(\\xi),\\, \\xi\\in (x_0,x_3) \\] <\/p>\n<blockquote><p><strong>Ejercicio:<\/strong> \u00bfCu\u00e1l es el \u00e1rea de la regi\u00f3n comprendida entre las curvas  \\(y=x^2-x\\) y \\(y=\\sqrt{x}\\)<\/p><\/blockquote>\n<p><script>\nfunction showHtmlDiv2() {\n  var htmlShow2 = document.getElementById(\"html-show2\");\n  if (htmlShow2.style.display === \"none\") {\n    htmlShow2.style.display = \"block\";\n  } else {\n    htmlShow2.style.display = \"none\";\n  }\n}\n<\/script> <\/p>\n<p><button onclick=\"showHtmlDiv2()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show2\" style=\"display: none;\">\n<!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i1)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">=<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">^<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_variable\">x<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">=<\/span><span class=\"code_function\">sqrt<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_function\">wxdraw2d<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">filled_func<\/span><span class=\"code_operator\">=<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">fill_color<\/span><span class=\"code_operator\">=<\/span><span class=\"code_variable\">grey<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_function\">explicit<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">x<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_number\">75<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">filled_func<\/span><span class=\"code_operator\">=<\/span><span class=\"code_function\">false<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">color<\/span><span class=\"code_operator\">=<\/span><span class=\"code_variable\">blue<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">line_width<\/span><span class=\"code_operator\">=<\/span><span class=\"code_number\">3<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_function\">explicit<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">x<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">filled_func<\/span><span class=\"code_operator\">=<\/span><span class=\"code_function\">false<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">color<\/span><span class=\"code_operator\">=<\/span><span class=\"code_variable\">red<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">line_width<\/span><span class=\"code_operator\">=<\/span><span class=\"code_number\">3<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_function\">explicit<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">x<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/uploads.jesussoto.es\/doc\/Ejer_area02_1.png\" width=\"1198\" style=\"max-width:90%;\" loading=\"lazy\" alt=\" (Graphics) \"\/><\/p>\n<p>\\[\\]<\/p>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">Por la gr\u00e1fica vemos que cero es un punto de intersecci\u00f3n, y el otro se encuentra en el intervalo [1.5,2]. Para conocerlo, utilizamos el m\u00e9todo de Newton:<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i5)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">define<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">fg<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_function\">define<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">newton<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_function\">fg<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_function\">diff<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">fg<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }\\operatorname{fg}(x)\\operatorname{:=}-{{x}^{2}}+x+\\sqrt{x}\\]<\/p>\n<p>\\[\\operatorname{ }\\operatorname{newton}(x)\\operatorname{:=}x-\\frac{-{{x}^{2}}+x+\\sqrt{x}}{-2 x+\\frac{1}{2 \\sqrt{x}}+1}\\]<\/p>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i8)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">fpprintprec<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">5<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_number\">5<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">newton<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">4<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }\\left[ 1.7982\\operatorname{,}1.7557\\operatorname{,}1.7548\\operatorname{,}1.7548\\right] \\]<\/p>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">La soluci\u00f3n que buscamos es p=1.7548.<\/p>\n<p>Ahora la regla de Simpson de 3\/8 en el intervalo [0,p].<\/p><\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i10) <\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">h<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">0<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">4<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">x0<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">0<\/span><span class=\"code_operator\">+<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">h<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">4<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }\\left[ 0\\operatorname{,}0.58495\\operatorname{,}1.1699\\operatorname{,}1.7548\\right] \\]<\/p>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i11) <\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">S<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">8<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">fg<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x0<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">4<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">numer<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[1.244\\]<\/p>\n<\/div>\n<hr \/>\n<h2>Regla \\(\\frac{2}{45}\\) de Simpson<\/h2>\n<p>\\[\\begin{multline*}\\int_{x_0}^{x_4} f(x) dx =\\frac{2h}{45}(7f(x_0)+32f(x_1)+12f(x_2)+32f(x_3)+7f(x_4))\\\\ -\\frac{8h^7}{945}f^{(6)}(\\xi),\\, \\xi\\in (x_0,x_4) \\}\\end{multline*}\\]<\/p>\n<blockquote><p><strong>Ejemplo:<\/strong> \u00bfCu\u00e1l es volumen aproximado de la funci\u00f3n \\(f(x)=x\\ \\sin(x^2)\\) alrededor de \\(0X\\), entre 0 y el corte con \\(x=0\\)?<\/p><\/blockquote>\n<p><script>\nfunction showHtmlDiv1t4() {\n  var htmlShow1t4 = document.getElementById(\"html-show1t4\");\n  if (htmlShow1t4.style.display === \"none\") {\n    htmlShow1t4.style.display = \"block\";\n  } else {\n    htmlShow1t4.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv1t4()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show1t4\" style=\"display: none;\">\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i2)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">=<\/span><span class=\"code_variable\">x<\/span><span class=\"code_endofline\">\u00b7<\/span><span class=\"code_function\">sin<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">^<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_function\">wxplot2d<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">x<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[{ }\\]<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/uploads.jesussoto.es\/maxima\/Ejer_768_Simpson10.png\" width=\"1198\" style=\"max-width:80%;\" loading=\"lazy\" alt=\" (Graphics) \"\/><!-- Text cell --><\/p>\n<div class=\"comment\">Determinemos el punto de corte con el eje OX. Como vemos, el corte est\u00e1 en el intervalo [1.5,2]<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i6)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">fpprintprec<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">5<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_function\">define<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">newton<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_function\">diff<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_number\">5<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">newton<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">6<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[{ }\\left[ 2.0696{,}1.6487{,}1.7976{,}1.7729{,}1.7724{,}1.7724\\right] \\]<\/p>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">Recordemos que el volumen de un s\u00f3lido que se genera por la revoluci\u00f3n sobre el eje OX de una curva \\(y=f(x)\\),y en nuestro caso, viene dado por \\[V= \\pi \\int_0^p f(x)^2\\,dx\\]<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i7)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">define<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">%pi<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">^<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[{ }{g}(x){:=}{\\pi}{{x}^{2}} {{\\sin{\\left( {{x}^{2}}\\right) }}^{2}}\\]<\/p>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">Ahora la regla de Simpson de 2\/45 en el intervalo [0,p].<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i10) <\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">n<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">5<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">0<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">x0<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">0<\/span><span class=\"code_operator\">+<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">h<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[{ }\\left[ 0{,}0.44311{,}0.88622{,}1.3293{,}1.7724\\right] \\]<\/p>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i12) <\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_operator\">(<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">45<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x0<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">7<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">32<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">12<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">32<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">7<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">%<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">numer<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[{ }3.6718\\]<\/p>\n<\/div>\n<hr \/>\n<h2>Regla de Simpson compuesta<\/h2>\n<p>\\[\\begin{multline*}\\int_a^b f(x) \\, dx=\\frac{h}{3}\\left[f(x_0)+2\\sum_{j=1}^{n\/2-1}f(x_{2j})+ 4\\sum_{j=1}^{n\/2}f(x_{2j-1})+f(x_n)\\right]\\\\ -(b-a)\\,\\frac{h^4}{180}\\,f^{(4)}(\\xi),\\,\\xi\\in (a,b)\\end{multline*}\\]<\/p>\n<blockquote><p><strong>Ejemplo:<\/strong> \u00bfCu\u00e1l es la longitud del arco aproximada de la funci\u00f3n \\(f(x)=x\\ \\sin(x^2)\\) en el intervalo \\([0,\\sqrt{\\pi}]\\)?<\/p>\n<p><strong>Nota<\/strong>: Para este ejercicio utilizaremos que, si una curva, definida por una funci\u00f3n \\({\\displaystyle f(x)}\\), y su respectiva derivada que son continuas en un intervalo \\({\\displaystyle [a,b]}\\), la longitud \\({\\displaystyle s}\\) del arco delimitado por \\(a\\) y \\(b\\) esta dada por la ecuaci\u00f3n \\[{\\displaystyle s=\\int _{a}^{b}{\\sqrt {1+\\left[f&#8217;\\left(x\\right)\\right]^{2}}}\\,{\\text{d}}x}\\]<\/p><\/blockquote>\n<p><script>\nfunction showHtmlDiv1t() {\n  var htmlShow1t = document.getElementById(\"html-show1t\");\n  if (htmlShow1t.style.display === \"none\") {\n    htmlShow1t.style.display = \"block\";\n  } else {\n    htmlShow1t.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv1t()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show1t\" style=\"display: none;\">\n<!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i2)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">=<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_function\">sin<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">^<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_function\">wxplot2d<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">x<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_function\">sqrt<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">%pi<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p><img decoding=\"async\" src=\"https:\/\/uploads.jesussoto.es\/2021\/11\/Ejer_regla_simpson_1.png\" width=\"1198\" style=\"max-width:80%;\" loading=\"lazy\" alt=\" (Graphics) \"\/><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i3)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">define<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_function\">sqrt<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">+<\/span><span class=\"code_function\">diff<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">^<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[{g}(x){:=}\\sqrt{{{\\left( \\sin{\\left( {{x}^{2}}\\right) }+2 {{x}^{2}} \\cos{\\left( {{x}^{2}}\\right) }\\right) }^{2}}+1}\\]<\/p>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">Ahora apliquemos la regla compuesta de Simpson, para n:40, en el intervalo [0,\\(\\sqrt{\\pi}\\)].<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i27) <\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">fpprintprec<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">5<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">40<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">sqrt<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">%pi<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">0<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">x0<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">0<\/span><span class=\"code_operator\">+<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">h<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x0<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">+<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">sum<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x0<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">+<\/span><span class=\"code_number\">4<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">sum<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x0<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">+<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">+<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x0<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">%<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">numer<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[3.4093\\]<\/p>\n<\/div>\n<hr \/>\n<h2>Regla de Simpson 3\/8 compuesta<\/h2>\n<p>Es m\u00e1s exacta que la regla de Simpson 3\/8 simple, ya que divide el intervalo de integraci\u00f3n en m\u00e1s subintervalos. Necesitamos la condici\u00f3n de que \\(n\\) sea m\u00faltiplo de 3.<\/p>\n<p>\\[\\int_a^b f(x) \\, dx\\approx {\\frac {3h}{8}}\\left[f(x_{0})+3\\sum _{i=0}^{{\\frac {n}{3}}-1}f(x_{3i+1})+3\\sum _{i=0}^{{\\frac {n}{3}}-1}f(x_{3i+2})+2\\sum _{i=0}^{{\\frac {n}{3}}-2}f(x_{3i+3})+f(x_{n})\\right]\\]<\/p>\n<blockquote><p><strong>Ejemplo:<\/strong> \u00bfCu\u00e1l es la superficie del volumen del s\u00f3lido que se genera por la revoluci\u00f3n sobre el eje OX de la curva \\(f(x)= \\cos(x^2)\\), entre y=0 y x=0?<\/p><\/blockquote>\n<p><script>\nfunction showHtmlDiv1tr() {\n  var htmlShow1tr = document.getElementById(\"html-show1tr\");\n  if (htmlShow1tr.style.display === \"none\") {\n    htmlShow1tr.style.display = \"block\";\n  } else {\n    htmlShow1tr.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv1tr()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show1tr\" style=\"display: none;\">\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i2)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">=<\/span><span class=\"code_function\">cos<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">^<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_function\">wxplot2d<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">x<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p><img decoding=\"async\" src=\"http:\/\/uploads.jesussoto.es\/maxima\/Ejer_768_Simpson11.png\" width=\"1198\" style=\"max-width:80%;\" loading=\"lazy\" alt=\" (Graphics) \"\/><\/p>\n<div class=\"comment\">Determinemos el punto de corte con el eje OX. Como vemos, el corte est\u00e1 en el intervalo [1,1.5]<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i6)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">fpprintprec<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">5<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_function\">define<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">newton<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_function\">diff<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_number\">5<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">newton<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">4<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\left[ 1.2308{,}1.2535{,}1.2533{,}1.2533\\right] \\]<\/p>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">Recordemos que la superficie del volumen de un s\u00f3lido que se genera por la revoluci\u00f3n sobre el eje OX de una curva \\(y=f(x)\\),y en nuestro caso, viene dado por \\[A=2\\pi\\int_a^b f(x) \\sqrt{1+\\left[f^\\prime(x)\\right]^2} \\, dx. \\]<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i7)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">define<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">%pi<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_function\">sqrt<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">+<\/span><span class=\"code_function\">diff<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">^<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[{g}(x){:=}2 {\\pi}\\cos{\\left( {{x}^{2}}\\right) } \\sqrt{4 {{x}^{2}} {{\\sin{\\left( {{x}^{2}}\\right) }}^{2}}+1}\\]<\/p>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">Ahora la regla de Simpson de 3\/8 compuesta en el intervalo [0,p].<\/p>\n<p>Observar que en la f\u00f3rmula n es m\u00faltiplo de 3, como nosotros partimos de 1, entonces n+1 tendr\u00e1 que ser m\u00faltiplo de 3:<\/p><\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i10) <\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">n<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_number\">5<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">p<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">0<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">x0<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">0<\/span><span class=\"code_operator\">+<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">h<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">Observemos como disponemos los \u00edndices:\\[{\\displaystyle I\\approx {\\frac {3h}{8}}\\left[f(x_{1})+3f(x_{2})+3f(x_{3})+2f(x_{4})+3f(x_{5})+3f(x_{6})+2f(x_{7})+\\dots +f(x_{n+1})\\right]}\\]<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i13) <\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">r2<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">r0<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">r1<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">+<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">n<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\left[ 2{,}5{,}8{,}11\\right] \\]<\/p>\n<p>\\[\\left[ 3{,}6{,}9{,}12\\right] \\]<\/p>\n<p>\\[\\left[ 4{,}7{,}10{,}13\\right] \\]<\/p>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i15) <\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_operator\">(<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">8<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x0<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">+<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_function\">sum<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x0<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">r2<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_function\">length<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">r2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">+<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_operator\">+<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_function\">sum<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x0<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">r0<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_function\">length<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">r0<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_operator\">+<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_function\">sum<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x0<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">r1<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_function\">length<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">r1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\"><br \/><\/span> \u00a0\u00a0 <span class=\"code_operator\">+<\/span><span class=\"code_function\">g<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x0<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">14<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">%<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">numer<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[7.4747\\]<\/p>\n<\/div>\n<hr \/>\n<table id=\"yzpi\" border=\"0\" width=\"100%\" cellspacing=\"0\" cellpadding=\"3\" bgcolor=\"#999999\">\n<tbody>\n<tr>\n<td width=\"100%\">\n<p><strong>Ejercicio:<\/strong>\u00bfCu\u00e1l es el volumen de un <a href=\"https:\/\/es.wikipedia.org\/wiki\/Casquete_esf%C3%A9rico\" target=\"_blank\" rel=\"noopener noreferrer\">casquete esf\u00e9rico<\/a>, si el radio de la esfera es \\(r=1\\) y la altura del casquete \\(h=0.2\\)?<\/p>\n<div id=\"menu-a\">\n<ul>\n<li>0.0689\\(\\pi\\)<\/li>\n<li>0.0125\\(\\pi\\)<\/li>\n<li>0.0373\\(\\pi\\)<\/li>\n<li>Ninguno de ellos<\/li>\n<\/ul>\n<\/div>\n<\/td>\n<td><a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Spherical_Cap.svg#\/media\/Archivo:Spherical_Cap.svg\"><img decoding=\"async\" loading=\"lazy\" class=\"\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/d\/d4\/Spherical_Cap.svg\/1200px-Spherical_Cap.svg.png\" alt=\"Spherical Cap.svg\" width=\"150\" height=\"150\" \/><\/a><br \/>\nDe <a href=\"\/\/commons.wikimedia.org\/wiki\/User:Pbroks13\" title=\"User:Pbroks13\"&gt;Pbroks13<\/a>User:Pbroks13 <a href=\"\/\/commons.wikimedia.org\/wiki\/File:Spherical_cap.gif\" title=\"File:Spherical cap.gif>Image:Spherical cap.gif<\/a>, Dominio p\u00fablico, <a href=\"https:\/\/commons.wikimedia.org\/w\/index.php?curid=5092574\">Enlace<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><script>\nfunction showHtmlDiv() {\n  var htmlShow = document.getElementById(\"html-show\");\n  if (htmlShow.style.display === \"none\") {\n    htmlShow.style.display = \"block\";\n  } else {\n    htmlShow.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<p><button onclick=\"showHtmlDiv()\">Soluci\u00f3n:<\/button><\/p>\n<div id=\"html-show\" style=\"display: none;\">\n<p><strong>C.)<\/strong><\/p>\n<div class=\"comment\">\n<p>Si observamos la figura vemos que el volumen que buscamos es la integral del \u00e1rea de los c\u00edrculos de radio \\(a\\): \\(V=\\int \\pi a^2\\ dh\\).<\/p>\n<\/div>\n<p><!-- Image cell --><\/p>\n<div class=\"image\">Figura 1:Casquete esf\u00e9rico<br \/><img decoding=\"async\" src=\"http:\/\/uploads.jesussoto.es\/2021\/11\/Ejer_volumen_casquete_0.png\" alt=\"Diagram\" style=\"max-width:90%;\" loading=\"lazy\"\/><\/div>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">\n<p>Por la relaci\u00f3n del tri\u00e1ngulo rect\u00e1ngulo de la figura, sabemos: \\((r-h)^2+a^2=r^2\\), luego<\/p>\n<\/div>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i1)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">A<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">h<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">r<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">=<\/span><span class=\"code_variable\">%pi<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">r<\/span><span class=\"code_operator\">^<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">r<\/span><span class=\"code_operator\">\u2212<\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">^<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }\\operatorname{A}\\left( h\\operatorname{,}r\\right) \\operatorname{:=}{\\pi}\\left( {{r}^{2}}-{{\\left( r-h\\right) }^{2}}\\right) \\]<\/p>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">Vamos a integrar sobre la altura, es decir; considerando r=1, como nos dice el enunciado y que h est\u00e9 en el intervalo [0,0.2]<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i2)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_function\">define<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">h<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_function\">ratsimp<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">A<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">h<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }\\operatorname{f}(h)\\operatorname{:=}2 {\\pi}h-{\\pi}{{h}^{2}}\\]<\/p>\n<p><!-- Text cell --><\/p>\n<div class=\"comment\">Utilicemos la regla de Simpson de 3\/8.<br \/>Si partimos de x0=0, tendremos un paso de (0.2-0)\/3<\/div>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i4)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">fpprintprec<\/span><span class=\"code_operator\">:<\/span><span class=\"code_number\">5<\/span><span class=\"code_endofline\">$<\/span><span class=\"code_endofline\"><br \/><\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">:<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">0<\/span><span class=\"code_operator\">+<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">3<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }\\left[ 0\\operatorname{,}0.066666\\operatorname{,}0.13333\\operatorname{,}0.2\\right] \\]<\/p>\n<p><!-- Code cell --><\/p>\n<table>\n<tr style=\"border: 0px;\">\n<td style=\"width: 70px;vertical-align: top;padding: 1mm;\"><span class=\"prompt\">(%i5)<\/span><\/td>\n<td style=\"vertical-align: top;padding: 1mm;\"><span class=\"input\"><span class=\"code_variable\">S<\/span><span class=\"code_operator\">:<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_operator\">(<\/span><span class=\"code_number\">0<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_number\">2<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">3<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\/<\/span><span class=\"code_number\">8<\/span><span class=\"code_operator\">)<\/span><span class=\"code_operator\">\u00b7<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">makelist<\/span><span class=\"code_operator\">(<\/span><span class=\"code_function\">f<\/span><span class=\"code_operator\">(<\/span><span class=\"code_variable\">x<\/span><span class=\"code_operator\">[<\/span><span class=\"code_variable\">i<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_variable\">i<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">4<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">.<\/span><span class=\"code_operator\">[<\/span><span class=\"code_number\">1<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">3<\/span><span class=\"code_endofline\">,<\/span><span class=\"code_number\">1<\/span><span class=\"code_operator\">]<\/span><span class=\"code_operator\">)<\/span><span class=\"code_endofline\">;<\/span><\/span><\/td>\n<\/tr>\n<\/table>\n<p>\\[\\operatorname{ }0.037333 {\\pi} \\]<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Regla del trapecio Muchas veces calcular la primitiva de una funci\u00f3n resulta tremendamente dif\u00edcil, cuando no imposible. En esos casos lo que hacemos en encontrar una aproximaci\u00f3n mediante m\u00e9todos de integraci\u00f3n num\u00e9rica&#8230;.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[5],"class_list":["post-498","post","type-post","status-publish","format-standard","hentry","category-mathbio","tag-practicas-mathbio"],"_links":{"self":[{"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/498","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=498"}],"version-history":[{"count":24,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/498\/revisions"}],"predecessor-version":[{"id":500,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/498\/revisions\/500"}],"wp:attachment":[{"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=498"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=498"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/clases.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=498"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}