{"id":395,"date":"2025-02-13T19:44:34","date_gmt":"2025-02-13T19:44:34","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/integration-formulas-and-the-net-change-theorem-apply-it\/"},"modified":"2025-02-13T19:44:34","modified_gmt":"2025-02-13T19:44:34","slug":"integration-formulas-and-the-net-change-theorem-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/integration-formulas-and-the-net-change-theorem-apply-it\/","title":{"raw":"Integration Formulas and the Net Change Theorem: Apply It","rendered":"Integration Formulas and the Net Change Theorem: Apply It"},"content":{"raw":"\n<section class=\"textbox learningGoals\">\n<ul>\n\t<li>Understand and apply the net change theorem to calculate how quantities change over an interval<\/li>\n\t<li>Use integration formulas to calculate the integrals of odd and even functions<\/li>\n<\/ul>\n<\/section>\n<h2>Exploring Integrals: From Basic Formulas to Advanced Applications<\/h2>\n<p>In this activity, we will delve into the world of integrals, a fundamental concept in calculus with diverse applications. From finding antiderivatives and calculating displacement to determining the properties of functions and evaluating definite integrals, integrals play a crucial role in understanding and solving real-world problems. This series of exercises will guide you through the process of evaluating indefinite integrals, applying the net change theorem, and exploring the behavior of functions through integration.&nbsp;<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p>[ohm_question hide_question_numbers=1]288334[\/ohm_question]<\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p>[ohm_question hide_question_numbers=1]288335[\/ohm_question]<\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p>[ohm_question hide_question_numbers=1]288336[\/ohm_question]<\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p>[ohm_question hide_question_numbers=1]288337[\/ohm_question]<\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p>[ohm_question hide_question_numbers=1]288338[\/ohm_question]<\/p>\n<\/section>\n","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Understand and apply the net change theorem to calculate how quantities change over an interval<\/li>\n<li>Use integration formulas to calculate the integrals of odd and even functions<\/li>\n<\/ul>\n<\/section>\n<h2>Exploring Integrals: From Basic Formulas to Advanced Applications<\/h2>\n<p>In this activity, we will delve into the world of integrals, a fundamental concept in calculus with diverse applications. From finding antiderivatives and calculating displacement to determining the properties of functions and evaluating definite integrals, integrals play a crucial role in understanding and solving real-world problems. This series of exercises will guide you through the process of evaluating indefinite integrals, applying the net change theorem, and exploring the behavior of functions through integration.&nbsp;<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288334\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288334&theme=lumen&iframe_resize_id=ohm288334&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288335\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288335&theme=lumen&iframe_resize_id=ohm288335&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288336\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288336&theme=lumen&iframe_resize_id=ohm288336&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288337\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288337&theme=lumen&iframe_resize_id=ohm288337&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<iframe loading=\"lazy\" id=\"ohm288338\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288338&theme=lumen&iframe_resize_id=ohm288338&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n","protected":false},"author":6,"menu_order":24,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":371,"module-header":"","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/395"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":0,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/395\/revisions"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/371"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/395\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=395"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=395"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=395"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=395"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}