{"id":154158,"date":"2022-03-25T23:13:27","date_gmt":"2022-03-25T17:43:27","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/area-between-two-curves-calculus-formula-and-calculation\/"},"modified":"2024-01-08T16:22:30","modified_gmt":"2024-01-08T10:52:30","slug":"area-between-two-curves-calculus-formula-and-calculation","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/area-between-two-curves-calculus\/","title":{"rendered":"Area Between Two Curves Calculus \u2013 Formula and Calculation"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-between-two-curves-calculus\/#Finding_the_Area_between_Two_Curves\" title=\"Finding the Area between Two Curves\">Finding the Area between Two Curves<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-between-two-curves-calculus\/#Formula_to_Find_the_Area_between_Two_Curves\" title=\"Formula to Find the Area between Two Curves\">Formula to Find the Area between Two Curves<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-between-two-curves-calculus\/#Calculating_Areas_Between_Two_Curves_by_Integration\" title=\"Calculating Areas Between Two Curves by Integration\">Calculating Areas Between Two Curves by Integration<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-between-two-curves-calculus\/#Calculating_Areas_Between_Curves_Using_Double_Integrals\" title=\"Calculating Areas Between Curves Using Double Integrals\">Calculating Areas Between Curves Using Double Integrals<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-between-two-curves-calculus\/#Solved_Example\" title=\"Solved Example\">Solved Example<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Finding_the_Area_between_Two_Curves\"><\/span>Finding the Area between Two Curves<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The area between two curves can be found by integrating the functions that define the curves. The region between the curves is the area between the x-axis and the curves, minus the areas of the two individual curves.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-154157 size-medium\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/area-between-two-curves-calculus-formula-and-calculation-300x212.jpg\" alt=\"Area Between Two Curves Calculus \u2013 Formula and Calculation\" width=\"300\" height=\"212\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/area-between-two-curves-calculus-formula-and-calculation-300x212.jpg?v=1648230203 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/area-between-two-curves-calculus-formula-and-calculation.jpg?v=1648230203 606w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Formula_to_Find_the_Area_between_Two_Curves\"><\/span>Formula to Find the Area between Two Curves<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The area between two curves can be found using the following formula:<\/p>\n<p>A = \u222b(f(x) \u2212 g(x))dx<\/p>\n<p>Where:<\/p>\n<p>A is the area between the curves<\/p>\n<p>f(x) is the function for the first curve<\/p>\n<p>g(x) is the function for the second curve<\/p>\n<p>dx is the differential of x<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Calculating_Areas_Between_Two_Curves_by_Integration\"><\/span>Calculating Areas Between Two Curves by Integration<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The area between two curves can be calculated by integration. The integration process involves finding the area of a set of small rectangles that cover the space between the curves. The height of each rectangle is equal to the difference in the y-values of the two curves at that point, and the width of each rectangle is equal to the difference in the x-values of the two curves at that point. Once the areas of all of the rectangles have been calculated, the total area between the curves can be found by adding up the individual rectangle areas.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Calculating_Areas_Between_Curves_Using_Double_Integrals\"><\/span>Calculating Areas Between Curves Using Double Integrals<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>We can use double integrals to calculate the area between two curves. Recall that a double integral is defined as<\/p>\n<p>where is a function of two variables and is a region in the coordinate plane.<\/p>\n<p>In order to calculate the area between two curves, we need to find the intersection of the two curves. We can then use the double integral to calculate the area between the curves and the x-axis.<\/p>\n<p>In the following example, we will calculate the area between the curves and the x-axis.<\/p>\n<p>Example<\/p>\n<p>Calculate the area between the curves and the x-axis.<\/p>\n<p>To calculate the area between the curves and the x-axis, we need to find the intersection of the two curves. We can do this by solving the equation of the curves for .<\/p>\n<p>We get the following intersection points:<\/p>\n<p>(0, 2)<\/p>\n<p>(3, 1)<\/p>\n<p>(6, 0)<\/p>\n<p>We can now use the double integral to calculate the area between the curves and the x-axis.<\/p>\n<p>We get the following result:<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Solved_Example\"><\/span>Solved Example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Q) The average of two numbers is 10. The sum of the two numbers is 20. What is the value of the two numbers?<\/p>\n<p>A) The two numbers are 5 and 15.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Finding the Area between Two Curves The area between two curves can be found by integrating the functions that define [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Area Between Two Curves Calculus","_yoast_wpseo_title":"Area Between Two Curves - Formula and Calculation","_yoast_wpseo_metadesc":"Learn about Area Between Two Curves Calculus topic of Maths in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/area-between-two-curves-calculus\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Area Between Two Curves - Formula and Calculation<\/title>\n<meta name=\"description\" content=\"Learn about Area Between Two Curves Calculus topic of Maths in details explained by subject experts on infinitylearn.com.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-between-two-curves-calculus\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Area Between Two Curves - 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