{"id":51,"date":"2009-01-19T12:00:18","date_gmt":"2009-01-19T17:00:18","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/crialmen\/?page_id=51"},"modified":"2009-03-03T11:34:49","modified_gmt":"2009-03-03T03:04:49","slug":"resolver-integrales","status":"publish","type":"page","link":"https:\/\/blog.espol.edu.ec\/crialmen\/resolver-integrales\/","title":{"rendered":"Resolver Integrales"},"content":{"rendered":"<ul>\n<li><span style=\"color: #00ff00\">Para resolver la Integrales definidas se usan varios metodos que acontinuacion se los va a nombrar y a explicar, y con ejemplos se los va a ilustrar para qeu el usuario lo entienda mejor.<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #00ff00\">Como ya se dijo antes para resolver una integral hay que de alguna forma llevar a una integral directa por eso existen estos metodos:<\/span><\/p>\n<ul> <object width=\"500\" height=\"405\"><param name=\"allowFullScreen\" value=\"true\" \/><param name=\"allowscriptaccess\" value=\"always\" \/><param name=\"src\" value=\"http:\/\/www.youtube-nocookie.com\/v\/fESUu8BXQaI&amp;hl=es&amp;fs=1&amp;color1=0x234900&amp;color2=0x4e9e00&amp;border=1\" \/><embed type=\"application\/x-shockwave-flash\" width=\"500\" height=\"405\" src=\"http:\/\/www.youtube-nocookie.com\/v\/fESUu8BXQaI&amp;hl=es&amp;fs=1&amp;color1=0x234900&amp;color2=0x4e9e00&amp;border=1\"><\/embed><\/object><\/p>\n<li><span style=\"color: #339966\"><strong>Regla Generalizada de las Potencias:<\/strong><\/span><\/li>\n<\/ul>\n<p><span style=\"color: #00ff00\">Si G es una funcio derivable y\u00a0n pertenece a los reales menos el -1 entonces la integral de :<\/span><\/p>\n<p><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"><span style=\"color: #339966\">\u222b<span> <\/span>((g(x))\u207f g \u00b4(x) dx = g(x)^n+1 \/ (n+1) <span> <\/span>+ C<\/span><\/span><\/p>\n<p><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"><span style=\"color: #339966\">Es decir si dentro de la integral se encuantra la funcion multiplicada por la derivada de la misma el resultado va a ser la funcion con el exponente que tenga sumado en uno dividida para el exponente sumado en uno mas a la constante. <\/span><\/span><\/p>\n<p><span style=\"color: #339966\">Ejemplo: <\/span><\/p>\n<p class=\"MsoListParagraphCxSpFirst\" style=\"margin: 0cm 0cm 0pt 36pt\"><span style=\"font-size: 16pt;color: #548dd4\"><span style=\"font-family: Book Antiqua\"> <span style=\"color: #00ff00\"> \u222bx^2 dx =<span> <\/span>X^3 \/ 3 +C <\/span><\/span><\/span><\/p>\n<p class=\"MsoListParagraphCxSpMiddle\" style=\"margin: 0cm 0cm 0pt 36pt\"><span style=\"font-size: 16pt;color: #548dd4\"><span style=\"font-family: Book Antiqua;color: #00ff00\"> <\/span><\/span><\/p>\n<p class=\"MsoListParagraphCxSpMiddle\" style=\"margin: 0cm 0cm 0pt 36pt\"><span style=\"font-size: 16pt;color: #548dd4\"><span style=\"font-family: Book Antiqua\"><span style=\"color: #00ff00\"><span> <\/span><span> <\/span><span> <\/span>\u222b Sin ^3(x) cos (x) dx = sin ^4(x)\/4 +C <\/span><\/span><\/span><\/p>\n<p class=\"MsoListParagraphCxSpMiddle\" style=\"margin: 0cm 0cm 0pt 36pt\">\n<p class=\"MsoListParagraphCxSpMiddle\" style=\"margin: 0cm 0cm 0pt 36pt\"><span style=\"font-size: large;font-family: Book Antiqua;color: #339966\">Integracion por Partes:<\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 12pt;color: #548dd4\"><span style=\"color: #00ff00\">Este m\u00e9todo normalmente se utiliza cuando en una integral existe un producto de funciones<\/span>.<\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 12pt;color: #548dd4\"><span style=\"color: #339966\">En este metodo hay que idntificar dos funciones:<\/span><\/span><\/p>\n<ul>\n<li>\n<div class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 12pt;color: #548dd4\"><span style=\"color: #339966\">Una Facil de derivar \u2192<\/span> <span style=\"color: #00ff00\">S<\/span><span style=\"color: #00ff00\">e va a llamar\u00a0U\u00a0\u00a0\u00a0\u00a0 Esta expresion se deriva<\/span><\/span><\/div>\n<\/li>\n<li>\n<div class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 12pt;color: #548dd4\"><span style=\"color: #339966\">Una facil de Integrar \u2192<\/span> <span style=\"color: #00ff00\">Se va a llamar dV\u00a0 Esta expresion se\u00a0integra <\/span><\/span><\/div>\n<\/li>\n<\/ul>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 12pt;color: #548dd4\"><span style=\"color: #00ff00\">Y\u00a0el resultado de la integra es el siguiente:<\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt;text-align: center\"><span style=\"font-size: 12pt;color: #548dd4\"><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"><span style=\"color: #339966\">\u222bf(x) g(x) dx= UV - \u222bVdU <\/span><\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 12pt;color: #548dd4\"><span style=\"color: #339966\">Ejemplo: <\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 16pt;color: #548dd4\"><span style=\"color: #00ff00\">\u222b ln (x) dx <\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 16pt;color: #548dd4\"><span style=\"color: #00ff00\">U = ln (x)<span> <\/span><span> <\/span>\u222bdV =\u222bdx<\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 16pt;color: #548dd4\"><span style=\"color: #00ff00\">dU= 1\/x dx<span> <\/span>V= x<\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 16pt;color: #548dd4\"><span style=\"color: #00ff00\">\u222b ln (x) dx = x ln (x) - \u222b x*(1\/x) dx <\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"color: #00ff00\"><span style=\"font-size: 16pt;color: #548dd4\"><span> <\/span><span> <\/span><span style=\"color: #00ff00\">= x ln (x) - <\/span><\/span><span style=\"font-size: 16pt;color: #00ff00\">\u222bdx<\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 16pt;color: #548dd4\"><span style=\"color: #00ff00\"><span> <\/span><span> <\/span>= x ln(x) \u2013 x <\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 16pt;color: #548dd4\"><span style=\"color: #00ff00\"><span> <\/span><span> <\/span>= x*( ln(x) -1) <\/span><\/span><\/p>\n<p><object width=\"500\" height=\"405\"><param name=\"allowFullScreen\" value=\"true\" \/><param name=\"allowscriptaccess\" value=\"always\" \/><param name=\"src\" value=\"http:\/\/www.youtube-nocookie.com\/v\/BOXqy71PQIg&amp;hl=es&amp;fs=1&amp;color1=0x234900&amp;color2=0x4e9e00&amp;border=1\" \/><embed type=\"application\/x-shockwave-flash\" width=\"500\" height=\"405\" src=\"http:\/\/www.youtube-nocookie.com\/v\/BOXqy71PQIg&amp;hl=es&amp;fs=1&amp;color1=0x234900&amp;color2=0x4e9e00&amp;border=1\"><\/embed><\/object><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\">\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 16pt\"><span style=\"color: #339966\">Integracion de Funciones Trigonometricas:<\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"color: #00ff00\">a) <\/span><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"><span style=\"color: #00ff00\">\u222bsin ^m(x)dx <\/span><span style=\"color: #00ff00\"><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\">\u222bcos^m(x) dx <\/span><\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"><span style=\"color: #00ff00\"><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"><span style=\"color: #00ff00\">Se uliliza las identidades\u00a0tirgonometricas dependiendo\u00a0del indice. <\/span> <\/span><\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"><span style=\"color: #00ff00\"><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"> <span style=\"color: #339966\"> m=Numero\u00a0impar\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 m=Numero \u00a0par <\/span><\/span><\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"><span style=\"color: #00ff00\">sin^2(x) = 1- cos^2(x)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0sin^2(x) = (1- cos(2x))\/2<\/span><\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"><span style=\"color: #00ff00\">con ^2(x) = 1- sin^2(x)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0cos^2(x) =\u00a0(1+cos(2x))\/2 <\/span><\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\"><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"><span style=\"color: #339966\">Ejemplo: <\/span><\/span><\/span><\/p>\n<p><span style=\"font-size: large;color: #00ff00\">\u222b sin^3(x) dx = \u222bsin ^2(x) sin (x) dx <\/span><\/p>\n<p><span style=\"font-size: large;color: #00ff00\"> = \u222b (1-cos^2(x)) sin(x) dx <\/span><\/p>\n<p><span style=\"font-size: large;color: #00ff00\"> = \u222bsin(x) dx - \u222b cos^2(x) sin (x) dx <\/span><\/p>\n<p><span style=\"font-size: large;color: #00ff00\">(por regla geeralizada\u00a0de la potencia) <\/span><\/p>\n<p><span style=\"font-size: large;color: #00ff00\"> = -cos (x) + cos ^3(x) \/3 +C <\/span><\/p>\n<p><span style=\"font-family: Arial;color: #00ff00;font-size: medium\"><\/p>\n<li><strong><a name=\"B\">Integrales racionales:<\/a><\/strong><\/li>\n<p><\/span><\/p>\n<p><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><strong><\/p>\n<p align=\"justify\">B.1.El grado del numerador P(x) es mayor que el grado del denominador Q(x)<\/p>\n<p><\/strong><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">Realizamos la divisi\u00f3n de P(x) por Q(x)  y llamando C(x) al cociente y R(x) al resto se ha de cumplir que:<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">P(x)=Q(x)C(x)+R(x)<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">Si R(x)=0 la divisi\u00f3n es exacta y si es distinto de cero el grado de R(x) ser\u00e1 menor que el grado de Q(x). Dividiendo la igualdad anterior por Q(x), tenemos:<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/usuarios.lycos.es\/manuelnando\/d2717.gif\" alt=\"\" width=\"134\" height=\"41\" \/><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">La integral se descompone en dos:<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/usuarios.lycos.es\/manuelnando\/d2718.gif\" alt=\"\" width=\"204\" height=\"41\" \/><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">Si la divisi\u00f3n es exacta, la integral ha quedado reducida a una inmediata de tipo potencial, si no lo es actuaremos como se explicar\u00e1 en el caso B.3.<\/span><\/p>\n<p><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><strong><\/p>\n<p align=\"justify\">B.2. El grado de P(x) es igual al grado de Q(x):<\/p>\n<p><\/strong><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">Entonces el cociente es una constante y la integral queda reducida a:<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/usuarios.lycos.es\/manuelnando\/d2719.gif\" alt=\"\" width=\"184\" height=\"41\" \/><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">La 1* inmediata y la segunda la estudiaremos en el caso B.2.<\/span><\/p>\n<p><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><strong><\/p>\n<p align=\"justify\">B.3. El grado de P(x) es menor que el grado de Q(x):<\/p>\n<p><\/strong><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">Seguimos el siguiente proceso:<\/span><\/p>\n<ul><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><\/p>\n<li>Obtenemos las ra\u00edces del polinomio denominador Q(x).y \u00e9stas pueden ser:<\/li>\n<p><\/span><\/ul>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">B.3.1. Ra\u00edces reales simples.<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">B.3.2. Ra\u00edces reales m\u00faltiples.<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">B.3.3. Ra\u00edces complejas simples.<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">B.3.4. Ra\u00edces complejas m\u00faltiples.<\/span><\/p>\n<p><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><strong><\/p>\n<p align=\"justify\">B.3.1. Ra\u00edces reales simples:<\/p>\n<p><\/strong><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">a) Podemos poner la integral racional as\u00ed:<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/usuarios.lycos.es\/manuelnando\/d2720.gif\" alt=\"\" width=\"509\" height=\"42\" \/><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">b) Descomponemos P(x)\/Q(x) en fracciones simples de la forma:<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/usuarios.lycos.es\/manuelnando\/d2721.gif\" alt=\"\" width=\"237\" height=\"42\" \/><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">c) Obtenemos los coeficientes A<sub>i<\/sub> expresando ambos miembros de la igualdad anterior en com\u00fan denominador que ser\u00e1 Q(x) y utilizando el m\u00e9todo de identificaci\u00f3n de coeficientes o dando valores a arbitrarios a x y resolviendo el sistema de ecuaciones que resulte.<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">d) Integramos el segundo miembro en el que todas las integrales que aparecen son inmediatas de tipo logaritmo neperiano.<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">Ejemplo:<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/usuarios.lycos.es\/manuelnando\/d2722.gif\" alt=\"\" width=\"93\" height=\"40\" \/><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">Hacemos:<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/usuarios.lycos.es\/manuelnando\/d2723.gif\" alt=\"\" width=\"538\" height=\"122\" \/><\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">Quedando la integral:<\/span><\/p>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/usuarios.lycos.es\/manuelnando\/d2724.gif\" alt=\"\" width=\"432\" height=\"40\" \/><\/span><\/p>\n<p align=\"justify\">\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><strong><\/p>\n<p align=\"justify\">En funciones  trigonom\u00e9tricas:<\/p>\n<p><\/strong><\/p>\n<p align=\"justify\">Para integrales del tipo <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/usuarios.lycos.es\/manuelnando\/d2775.gif\" alt=\"\" width=\"134\" height=\"33\" \/><\/p>\n<p><\/span><\/p>\n<table border=\"1\" cellspacing=\"1\" cellpadding=\"4\" width=\"391\">\n<tbody>\n<tr>\n<td width=\"59%\" valign=\"top\">\n<p align=\"justify\"><span style=\"color: #00ff00\"><strong><span style=\"font-family: Arial;font-size: xx-small\">Sustituci\u00f3n<\/span><\/strong><\/span><\/p>\n<\/td>\n<td width=\"41%\" valign=\"top\">\n<p align=\"justify\"><span style=\"color: #00ff00\"><strong><span style=\"font-family: Arial;font-size: xx-small\">C\u00e1lculo de los elementos<\/span><\/strong><\/span><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"59%\" valign=\"top\">\n<ul><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><\/p>\n<li>Si R(sen x, cos x) es impar en sen x<\/li>\n<p><\/span><\/ul>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">Hacemos cos x=t<\/span><\/p>\n<\/td>\n<td width=\"41%\" valign=\"top\">\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/usuarios.lycos.es\/manuelnando\/d2776.gif\" alt=\"\" width=\"105\" height=\"72\" \/><\/span><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"59%\" valign=\"top\">\n<ul><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><\/p>\n<li>Si R(sen x, cos x) es impar en cos x<\/li>\n<p><\/span><\/ul>\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\">Hacemos sen x=t<\/span><\/p>\n<\/td>\n<td width=\"41%\" valign=\"top\">\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/usuarios.lycos.es\/manuelnando\/d2777.gif\" alt=\"\" width=\"104\" height=\"72\" \/><\/span><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"59%\" valign=\"top\">\n<ul><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><\/p>\n<li>Si R(sen x, cos x) es par en sen x y cos x hacemos tg x=t<\/li>\n<p><\/span><\/ul>\n<\/td>\n<td width=\"41%\" valign=\"top\">\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/usuarios.lycos.es\/manuelnando\/d2778.gif\" alt=\"\" width=\"108\" height=\"130\" \/><\/span><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"59%\" valign=\"top\">\n<ul><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><\/p>\n<li>Si R(sen x, cos x) no cumple ninguna de las caracter\u00edsticas anteriores hacemos <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/usuarios.lycos.es\/manuelnando\/d2779.gif\" alt=\"\" width=\"56\" height=\"38\" \/><\/li>\n<p><\/span><\/ul>\n<\/td>\n<td width=\"41%\" valign=\"top\">\n<p align=\"justify\"><span style=\"font-family: Arial;color: #00ff00;font-size: xx-small\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/usuarios.lycos.es\/manuelnando\/d2780.gif\" alt=\"\" width=\"96\" height=\"124\" \/><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div><span style=\"color: #548dd4\"> <\/span><\/div>\n<p><span style=\"color: #548dd4\"> <\/span><\/p>\n<div><span style=\"color: #548dd4\"> <\/span><\/div>\n<p><span style=\"color: #548dd4\"> <\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\">\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\">\n<p><span style=\"font-size: 12pt;color: #548dd4\"><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"> <\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\">\n<div><span style=\"font-size: large;font-family: Book Antiqua;color: #339966\"> <\/span><\/div>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\">\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\">\n<p><span style=\"font-size: 12pt;color: #548dd4\"><span style=\"font-size: 16pt;font-family: &quot;Book Antiqua&quot;,&quot;serif&amp;quot&quot;color: #548dd4\"> <\/span><\/span><\/p>\n<p class=\"MsoNormal\" style=\"margin: 0cm 0cm 10pt\">\n","protected":false},"excerpt":{"rendered":"<p>Para resolver la Integrales definidas se usan varios metodos que acontinuacion se los va a nombrar y a explicar, y con ejemplos se los va a ilustrar para qeu el usuario lo entienda mejor. Como ya se dijo antes para resolver una integral hay que de alguna forma llevar a una integral directa por eso [&hellip;]<\/p>\n","protected":false},"author":809,"featured_media":0,"parent":0,"menu_order":3,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-51","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/crialmen\/wp-json\/wp\/v2\/pages\/51","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/crialmen\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/crialmen\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/crialmen\/wp-json\/wp\/v2\/users\/809"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/crialmen\/wp-json\/wp\/v2\/comments?post=51"}],"version-history":[{"count":11,"href":"https:\/\/blog.espol.edu.ec\/crialmen\/wp-json\/wp\/v2\/pages\/51\/revisions"}],"predecessor-version":[{"id":53,"href":"https:\/\/blog.espol.edu.ec\/crialmen\/wp-json\/wp\/v2\/pages\/51\/revisions\/53"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/crialmen\/wp-json\/wp\/v2\/media?parent=51"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}