{"id":7242,"date":"2025-12-02T12:08:35","date_gmt":"2025-12-02T18:08:35","guid":{"rendered":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/?page_id=7242"},"modified":"2025-12-02T13:18:08","modified_gmt":"2025-12-02T19:18:08","slug":"m2l14","status":"publish","type":"page","link":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/lecciones-m2\/m2l14\/","title":{"rendered":"m2l14"},"content":{"rendered":"\n<h1>14 Teorema fundamental<\/h1>\n\n\n\n<p>Para definir la integral definida, seg\u00fan se vio, se utiliz\u00f3 el l\u00edmite de sumas parciales, en este caso, de \u00e1reas de rect\u00e1ngulos, pero no por ello, el l\u00edmite de sumas parciales, es el procedimiento id\u00f3neo y recomendable para el calcular integrales definidas.<\/p>\n\n\n\n<p>El problema de calcular integrales definidas por el l\u00edmite de sumas queda resuelto por el procedimiento para calcular integrales definidas sin el empleo de \u00e9ste. Este procedimiento est\u00e1 descrito en el teorema fundamental del c\u00e1lculo, el cual conecta dos conceptos claves del c\u00e1lculo, la integral y la derivada. La derivada nos lleva, por ejemplo, de la distancia a la velocidad en cualquier instante y la integral nos lleva de la velocidad en cada instante a la distancia total.<\/p>\n\n\n\n<p>Con el teorema fundamental del c\u00e1lculo, descubierto por Newton y Leibniz, se fortalecieron distintas ramas de las matem\u00e1ticas y conduce a innumerables aplicaciones en las ciencias naturales, por ejemplo. Por este descubrimiento a Newton y Leibniz se les considera inventores del c\u00e1lculo infinitesimal.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-155.png?w=745\" alt=\"\" class=\"wp-image-707\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-156.png?w=604\" alt=\"\" class=\"wp-image-708\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-157.png?w=746\" alt=\"\" class=\"wp-image-710\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-158.png?w=609\" alt=\"\" class=\"wp-image-711\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-159.png?w=713\" alt=\"\" class=\"wp-image-713\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-160.png?w=691\" alt=\"\" class=\"wp-image-714\" \/><\/figure>\n\n\n\n<h2 id=\"derivada-de-una-integral\">Derivada de una Integral<\/h2>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-161.png?w=556\" alt=\"\" class=\"wp-image-716\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-162.png?w=728\" alt=\"\" class=\"wp-image-717\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-163.png?w=224\" alt=\"\" class=\"wp-image-718\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-164.png?w=430\" alt=\"\" class=\"wp-image-720\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-165.png?w=548\" alt=\"\" class=\"wp-image-721\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-166.png?w=743\" alt=\"\" class=\"wp-image-722\" \/><\/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\/11\/image-167.png?w=435\" alt=\"\" class=\"wp-image-724\" \/><\/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\/m2l15\/\">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>14 Teorema fundamental Para definir la integral definida, seg\u00fan se vio, se utiliz\u00f3 el l\u00edmite de sumas parciales, en este caso, de \u00e1reas de rect\u00e1ngulos, pero no por ello, el l\u00edmite de sumas parciales, es el procedimiento id\u00f3neo y recomendable para el calcular integrales definidas. El problema de calcular integrales definidas por el l\u00edmite de &hellip; <a href=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/lecciones-m2\/m2l14\/\" class=\"more-link\">Contin\u00faa leyendo <span class=\"screen-reader-text\">m2l14<\/span><\/a><\/p>\n","protected":false},"author":123458,"featured_media":0,"parent":7208,"menu_order":14,"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\/7242"}],"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=7242"}],"version-history":[{"count":2,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/7242\/revisions"}],"predecessor-version":[{"id":7278,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/7242\/revisions\/7278"}],"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=7242"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}