{"id":3469,"date":"2024-06-24T16:54:10","date_gmt":"2024-06-24T16:54:10","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus1\/?post_type=chapter&#038;p=3469"},"modified":"2025-08-18T01:45:19","modified_gmt":"2025-08-18T01:45:19","slug":"areas-between-curves-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus1\/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>\r\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>\r\n<center>\r\n[caption id=\"attachment_3998\" align=\"aligncenter\" width=\"905\"]<img class=\"wp-image-3998 size-full\" 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\" \/> Images of prominent female athletes[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\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>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]288024[\/ohm_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p>[ohm_question hide_question_numbers=1]288057[\/ohm_question]<\/p>\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;\">\n<figure id=\"attachment_3998\" aria-describedby=\"caption-attachment-3998\" style=\"width: 905px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3998 size-full\" 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\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16194941\/Screenshot-2024-07-16-154832.png 905w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16194941\/Screenshot-2024-07-16-154832-300x134.png 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16194941\/Screenshot-2024-07-16-154832-768x343.png 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16194941\/Screenshot-2024-07-16-154832-65x29.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16194941\/Screenshot-2024-07-16-154832-225x100.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/34\/2024\/06\/16194941\/Screenshot-2024-07-16-154832-350x156.png 350w\" sizes=\"(max-width: 905px) 100vw, 905px\" \/><figcaption id=\"caption-attachment-3998\" class=\"wp-caption-text\">Images of prominent female athletes<\/figcaption><\/figure>\n<\/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\">\n<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><br \/>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<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><br \/>\n<\/section>\n","protected":false},"author":15,"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":407,"module-header":"apply_it","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\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3469"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":6,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3469\/revisions"}],"predecessor-version":[{"id":4798,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3469\/revisions\/4798"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/parts\/407"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapters\/3469\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/media?parent=3469"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/pressbooks\/v2\/chapter-type?post=3469"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/contributor?post=3469"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus1\/wp-json\/wp\/v2\/license?post=3469"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}