{"id":429,"date":"2025-02-13T19:44:51","date_gmt":"2025-02-13T19:44:51","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/areas-between-curves-apply-it\/"},"modified":"2026-02-04T15:20:30","modified_gmt":"2026-02-04T15:20:30","slug":"areas-between-curves-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/areas-between-curves-apply-it\/","title":{"raw":"Areas Between Curves: Apply It","rendered":"Areas Between Curves: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Calculate the area between two curves by integrating with respect to [latex]x[\/latex]<\/li>\r\n \t<li>Calculate the area of a compound region<\/li>\r\n \t<li>Calculate the area between two curves by integrating with respect to [latex]y[\/latex]<\/li>\r\n \t<li>Determine the most effective variable, [latex]x[\/latex] or [latex]y[\/latex], for integration based on the curves\u2019 orientation<\/li>\r\n<\/ul>\r\n<\/section>Sydney Michelle McLaughlin-Levrone and Femke Bol are track and field athletes who both hold world records and compete in sprint events.\r\n\r\n<center><img class=\"size-full wp-image-3998 aligncenter\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16194941\/Screenshot-2024-07-16-154832.png\" alt=\"On the left, McLaughlin-Levrone competing at the 2022 World Athletics Championships, running on a track with a focused expression. On the right, Bol smiling and holding her gold medal for the 400m hurdles at the 2023 World Championships in Budapest.&quot;\" width=\"905\" height=\"404\" \/><\/center>&nbsp;\r\n\r\nSuppose they were to run a long distance race rather than a sprint. In a sprint, runners accelerate quickly and maintain a very high velocity for a relatively short distance, whereas in a long distance race, endurance is key, and so runners must take a different approach to velocity and acceleration.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]288024[\/ohm_question]\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]288057[\/ohm_question]\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Calculate the area between two curves by integrating with respect to [latex]x[\/latex]<\/li>\n<li>Calculate the area of a compound region<\/li>\n<li>Calculate the area between two curves by integrating with respect to [latex]y[\/latex]<\/li>\n<li>Determine the most effective variable, [latex]x[\/latex] or [latex]y[\/latex], for integration based on the curves\u2019 orientation<\/li>\n<\/ul>\n<\/section>\n<p>Sydney Michelle McLaughlin-Levrone and Femke Bol are track and field athletes who both hold world records and compete in sprint events.<\/p>\n<div style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-3998 aligncenter\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16194941\/Screenshot-2024-07-16-154832.png\" alt=\"On the left, McLaughlin-Levrone competing at the 2022 World Athletics Championships, running on a track with a focused expression. On the right, Bol smiling and holding her gold medal for the 400m hurdles at the 2023 World Championships in Budapest.&quot;\" width=\"905\" height=\"404\" \/><\/div>\n<p>&nbsp;<\/p>\n<p>Suppose they were to run a long distance race rather than a sprint. In a sprint, runners accelerate quickly and maintain a very high velocity for a relatively short distance, whereas in a long distance race, endurance is key, and so runners must take a different approach to velocity and acceleration.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm288024\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288024&theme=lumen&iframe_resize_id=ohm288024&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm288057\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=288057&theme=lumen&iframe_resize_id=ohm288057&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":6,"menu_order":8,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":421,"module-header":"- Select 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\/429"}],"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":3,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/429\/revisions"}],"predecessor-version":[{"id":2543,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/429\/revisions\/2543"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/421"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/429\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=429"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=429"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=429"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=429"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}