{"id":7246,"date":"2025-12-02T12:08:52","date_gmt":"2025-12-02T18:08:52","guid":{"rendered":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/?page_id=7246"},"modified":"2025-12-02T13:18:28","modified_gmt":"2025-12-02T19:18:28","slug":"m2l16","status":"publish","type":"page","link":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/lecciones-m2\/m2l16\/","title":{"rendered":"m2l16"},"content":{"rendered":"\n<h1>16 M\u00e9todos de Integraci\u00f3n<\/h1>\n\n\n\n<p>El integrando puede ser una funci\u00f3n tal que es posible obtener la antiderivada por integraci\u00f3n inmediata o sea tal que por alg\u00fan m\u00e9todo de integraci\u00f3n se puede reducir a obtener la antiderivada por integraci\u00f3n inmediata o sea tan dif\u00edcil que es imposible obtener la antiderivada. Cuando esto ocurre, num\u00e9ricamente, se puede obtener un valor apropiado.<\/p>\n\n\n\n<p>Despu\u00e9s de haber revisado el m\u00e9todo de integraci\u00f3n inmediata, ahora se estudia el m\u00e9todo de sustituci\u00f3n o cambio de variable.<\/p>\n\n\n\n<p>La regla de la cadena es fundamental en el m\u00e9todo de la sustituci\u00f3n. Esto es,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image.png?w=562\" alt=\"\" class=\"wp-image-742\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-1.png?w=773\" alt=\"\" class=\"wp-image-743\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-2.png?w=600\" alt=\"\" class=\"wp-image-745\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-3.png?w=691\" alt=\"\" class=\"wp-image-746\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-4.png?w=737\" alt=\"\" class=\"wp-image-747\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-5.png?w=767\" alt=\"\" class=\"wp-image-749\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-6.png?w=766\" alt=\"\" class=\"wp-image-750\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-7.png?w=753\" alt=\"\" class=\"wp-image-751\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-8.png?w=754\" alt=\"\" class=\"wp-image-753\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-9.png?w=638\" alt=\"\" class=\"wp-image-754\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-10.png?w=752\" alt=\"\" class=\"wp-image-756\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-11.png?w=753\" alt=\"\" class=\"wp-image-757\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-12.png?w=757\" alt=\"\" class=\"wp-image-759\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-13.png?w=765\" alt=\"\" class=\"wp-image-760\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-14.png?w=641\" alt=\"\" class=\"wp-image-761\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-15.png?w=773\" alt=\"\" class=\"wp-image-763\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-16.png?w=745\" alt=\"\" class=\"wp-image-764\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-17.png?w=762\" alt=\"\" class=\"wp-image-766\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-18.png?w=754\" alt=\"\" class=\"wp-image-767\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-19.png?w=754\" alt=\"\" class=\"wp-image-768\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-20.png?w=739\" alt=\"\" class=\"wp-image-770\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-21.png?w=678\" alt=\"\" class=\"wp-image-771\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-22.png?w=746\" alt=\"\" class=\"wp-image-773\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-23.png?w=766\" alt=\"\" class=\"wp-image-774\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-24.png?w=755\" alt=\"\" class=\"wp-image-775\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-25.png?w=751\" alt=\"\" class=\"wp-image-776\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-26.png?w=730\" alt=\"\" class=\"wp-image-778\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-27.png?w=698\" alt=\"\" class=\"wp-image-779\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-28.png?w=576\" alt=\"\" class=\"wp-image-781\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-29.png?w=743\" alt=\"\" class=\"wp-image-782\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-30.png?w=746\" alt=\"\" class=\"wp-image-783\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-31.png?w=629\" alt=\"\" class=\"wp-image-785\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-32.png?w=745\" alt=\"\" class=\"wp-image-786\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-33.png?w=728\" alt=\"\" class=\"wp-image-787\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-34.png?w=736\" alt=\"\" class=\"wp-image-789\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-35.png?w=756\" alt=\"\" class=\"wp-image-791\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-36.png?w=739\" alt=\"\" class=\"wp-image-792\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-37.png?w=737\" alt=\"\" class=\"wp-image-793\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-38.png?w=749\" alt=\"\" class=\"wp-image-794\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-39.png?w=758\" alt=\"\" class=\"wp-image-796\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-40.png?w=516\" alt=\"\" class=\"wp-image-797\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-41.png?w=738\" alt=\"\" class=\"wp-image-798\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-42.png?w=745\" alt=\"\" class=\"wp-image-800\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-43.png?w=497\" alt=\"\" class=\"wp-image-801\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-44.png?w=763\" alt=\"\" class=\"wp-image-802\" \/><\/figure>\n\n\n\n<h2 id=\"integral-definida\">Integral definida<\/h2>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-45.png?w=759\" alt=\"\" class=\"wp-image-804\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-46.png?w=754\" alt=\"\" class=\"wp-image-805\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-47.png?w=705\" alt=\"\" class=\"wp-image-807\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-48.png?w=754\" alt=\"\" class=\"wp-image-808\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-49.png?w=764\" alt=\"\" class=\"wp-image-809\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-50.png?w=742\" alt=\"\" class=\"wp-image-811\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-51.png?w=757\" alt=\"\" class=\"wp-image-812\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-52.png?w=748\" alt=\"\" class=\"wp-image-814\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-53.png?w=406\" alt=\"\" class=\"wp-image-815\" \/><\/figure>\n\n\n\n<h2 id=\"tarea\">Tarea<\/h2>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/12\/image-54.png?w=415\" alt=\"\" class=\"wp-image-817\" \/><\/figure>\n\n\n\n<div class=\"is-layout-flex wp-block-buttons\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/m2l17\/\">siguiente<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/lecciones-m2\/\">lecciones<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>16 M\u00e9todos de Integraci\u00f3n El integrando puede ser una funci\u00f3n tal que es posible obtener la antiderivada por integraci\u00f3n inmediata o sea tal que por alg\u00fan m\u00e9todo de integraci\u00f3n se puede reducir a obtener la antiderivada por integraci\u00f3n inmediata o sea tan dif\u00edcil que es imposible obtener la antiderivada. Cuando esto ocurre, num\u00e9ricamente, se puede &hellip; <a href=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/lecciones-m2\/m2l16\/\" class=\"more-link\">Contin\u00faa leyendo <span class=\"screen-reader-text\">m2l16<\/span><\/a><\/p>\n","protected":false},"author":123458,"featured_media":0,"parent":7208,"menu_order":16,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0},"_links":{"self":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/7246"}],"collection":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/users\/123458"}],"replies":[{"embeddable":true,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/comments?post=7246"}],"version-history":[{"count":2,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/7246\/revisions"}],"predecessor-version":[{"id":7282,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/7246\/revisions\/7282"}],"up":[{"embeddable":true,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/7208"}],"wp:attachment":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/media?parent=7246"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}