{"id":379,"date":"2025-02-13T19:44:27","date_gmt":"2025-02-13T19:44:27","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/approximating-areas-apply-it\/"},"modified":"2025-02-13T19:44:27","modified_gmt":"2025-02-13T19:44:27","slug":"approximating-areas-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/approximating-areas-apply-it\/","title":{"raw":"Approximating Areas: Apply It","rendered":"Approximating Areas: Apply It"},"content":{"raw":"\n<section class=\"textbox learningGoals\">\n<ul>\n\t<li>Estimate the area under a curve by adding up the areas of rectangles<\/li>\n\t<li>Estimate the area under a curve using Riemann sums<\/li>\n<\/ul>\n<\/section>\n<h2>Exploring Area Under Curves with Riemann Sums<\/h2>\n<p>In this apply-it task, we'll dive into the concept of Riemann sums and their application in approximating the area under curves. We'll explore how different choices of evaluation points affect our estimates and how increasing the number of subintervals improves our approximation. This exercise will help you understand the foundation of integral calculus and its connection to finding areas of complex shapes.<br>\n<br>\n<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p>[ohm_question hide_question_numbers=1]288324[\/ohm_question]<\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p>[ohm_question hide_question_numbers=1]288325[\/ohm_question]<\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p>[ohm_question hide_question_numbers=1]288326[\/ohm_question]<\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p>[ohm_question hide_question_numbers=1]288327[\/ohm_question]<\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p>[ohm_question hide_question_numbers=1]288328[\/ohm_question]<\/p>\n<\/section>\n","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Estimate the area under a curve by adding up the areas of rectangles<\/li>\n<li>Estimate the area under a curve using Riemann sums<\/li>\n<\/ul>\n<\/section>\n<h2>Exploring Area Under Curves with Riemann Sums<\/h2>\n<p>In this apply-it task, we&#8217;ll dive into the concept of Riemann sums and their application in approximating the area under curves. We&#8217;ll explore how different choices of evaluation points affect our estimates and how increasing the number of subintervals improves our approximation. 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