{"id":7236,"date":"2025-12-02T12:08:09","date_gmt":"2025-12-02T18:08:09","guid":{"rendered":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/?page_id=7236"},"modified":"2025-12-02T13:17:38","modified_gmt":"2025-12-02T19:17:38","slug":"m2l11","status":"publish","type":"page","link":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/lecciones-m2\/m2l11\/","title":{"rendered":"m2l11"},"content":{"rendered":"\n<h1>11 Series e Integral Definida<\/h1>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-94.png?w=790\" alt=\"\" class=\"wp-image-614\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-95.png?w=845\" alt=\"\" class=\"wp-image-616\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-96.png?w=861\" alt=\"\" class=\"wp-image-617\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-97.png?w=839\" alt=\"\" class=\"wp-image-619\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-98.png?w=826\" alt=\"\" class=\"wp-image-620\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-99.png?w=834\" alt=\"\" class=\"wp-image-621\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-100.png?w=851\" alt=\"\" class=\"wp-image-622\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-101.png?w=827\" alt=\"\" class=\"wp-image-624\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-102.png?w=722\" alt=\"\" class=\"wp-image-626\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-103.png?w=609\" alt=\"\" class=\"wp-image-627\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-104.png?w=737\" alt=\"\" class=\"wp-image-628\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-105.png?w=850\" alt=\"\" class=\"wp-image-629\" \/><\/figure>\n\n\n\n<h2 id=\"integral-definida\">Integral Definida<\/h2>\n\n\n\n<p>Despu\u00e9s de haber estudiado brevemente a las series num\u00e9ricas y series de potencias, y los criterios de convergencia; ahora estudiaremos a la integral y sus propiedades. Para tal efecto, se debe contar con los conocimientos, entre otros y, sobre todo, del \u00e1lgebra de los n\u00fameros reales, funciones, l\u00edmites y derivadas; los cuales contribuyen a tener menos dificultades en la comprensi\u00f3n de los temas y, consecuentemente, mayores posibilidades de \u00e9xito.<\/p>\n\n\n\n<p>Antes de iniciar con el tema es conveniente hacer una reflexi\u00f3n sobre el mismo. En este sentido se formula el siguiente cuestionamiento.<\/p>\n\n\n\n<ul>\n<li>\u00bfSabes c\u00f3mo se define una integral?<\/li>\n\n\n\n<li>\u00bfQu\u00e9 propiedades conoces de esto?<\/li>\n\n\n\n<li>\u00bfCu\u00e1l es el significado de integral definida?<\/li>\n\n\n\n<li>\u00bfQu\u00e9 interpretaci\u00f3n tiene la integral definida?<\/li>\n\n\n\n<li>\u00bfQu\u00e9 relaci\u00f3n tiene la integral definida con el \u00e1rea?<\/li>\n\n\n\n<li>\u00bfCu\u00e1ndo surge la noci\u00f3n anal\u00edtica de la integral definida?<\/li>\n\n\n\n<li>\u00bfEn qu\u00e9, el \u00e1rea de una regi\u00f3n con fronteras curvas encuentra su formulaci\u00f3n matem\u00e1tica?<\/li>\n\n\n\n<li>\u00bfQu\u00e9 relaci\u00f3n tiene la integral definida con el l\u00edmite?<\/li>\n\n\n\n<li>\u00bfCu\u00e1les son los conceptos centrales del c\u00e1lculo?<\/li>\n\n\n\n<li>\u00bfCu\u00e1l es el concepto fundamental del c\u00e1lculo integral?<\/li>\n\n\n\n<li>\u00bfCu\u00e1l es el concepto fundamental del c\u00e1lculo diferencial?<\/li>\n\n\n\n<li>\u00bfC\u00f3mo son los procesos de derivaci\u00f3n e integraci\u00f3n?<\/li>\n\n\n\n<li>\u00bfQu\u00e9 teorema relaciona a la integral y la derivada?<\/li>\n\n\n\n<li>\u00bfTendr\u00e1 aplicaci\u00f3n este concepto?<\/li>\n\n\n\n<li>\u00bfVale la pena estudiar c\u00e1lculo?<\/li>\n\n\n\n<li>\u00bfEstas preguntas te generaron alguna inquietud positiva?<\/li>\n<\/ul>\n\n\n\n<p>A trav\u00e9s de ejemplos sencillos, se construye el concepto de integral definida.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-106.png?w=853\" alt=\"\" class=\"wp-image-632\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-107.png?w=859\" alt=\"\" class=\"wp-image-633\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/paramate2.wordpress.com\/wp-content\/uploads\/2021\/11\/image-108.png?w=866\" alt=\"\" class=\"wp-image-635\" \/><\/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-109.png?w=866\" alt=\"\" class=\"wp-image-636\" \/><\/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\/m2l12\/\">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>11 Series e Integral Definida Integral Definida Despu\u00e9s de haber estudiado brevemente a las series num\u00e9ricas y series de potencias, y los criterios de convergencia; ahora estudiaremos a la integral y sus propiedades. Para tal efecto, se debe contar con los conocimientos, entre otros y, sobre todo, del \u00e1lgebra de los n\u00fameros reales, funciones, l\u00edmites &hellip; <a href=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/lecciones-m2\/m2l11\/\" class=\"more-link\">Contin\u00faa leyendo <span class=\"screen-reader-text\">m2l11<\/span><\/a><\/p>\n","protected":false},"author":123458,"featured_media":0,"parent":7208,"menu_order":11,"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\/7236"}],"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=7236"}],"version-history":[{"count":3,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/7236\/revisions"}],"predecessor-version":[{"id":7272,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/7236\/revisions\/7272"}],"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=7236"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}