{"id":133898,"date":"2023-03-11T18:21:58","date_gmt":"2023-03-11T12:51:58","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=133898"},"modified":"2023-03-11T18:21:58","modified_gmt":"2023-03-11T12:51:58","slug":"using-integration-find-th-e-area-of-the-region-bounded-by-y-m-m-0-x-1-x-2-and-the-x-axis","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/quiz\/using-integration-find-th-e-area-of-the-region-bounded-by-y-m-m-0-x-1-x-2-and-the-x-axis","title":{"rendered":"Using integration, find th e area of the region bounded by y = m (m > 0), x = 1, x = 2 and the x-axis."},"content":{"rendered":"<h2>Question: Using integration, find th e area of the region bounded by y = m (m &gt; 0), x = 1, x = 2 and the x-axis.<\/h2>\n<p>&nbsp;<\/p>\n<h3>The correct answer is &#8211;<\/h3>\n<h3>To find the area of the region bounded by the lines y = m, x = 1, x = 2, and the x-axis, we need to integrate the area of the vertical strips that make up the region.<\/h3>\n<h3>Since the line y = m is parallel to the x-axis, the height of each strip is a constant value of m. The width of each strip is dx. Therefore, the area of each strip is dA = m dx.<\/h3>\n<h3>The limits of integration for x are 1 and 2, so the total area of the region is given by:<\/h3>\n<h3>A = \u222b(from x=1 to x=2) m dx<\/h3>\n<h3>A = m[x] from x=1 to x=2<\/h3>\n<h3>A = m(2 &#8211; 1)<\/h3>\n<h3>A = m<\/h3>\n<h3>Therefore, the area of the region bounded by y = m, x = 1, x = 2, and the x-axis is equal to m square units.<\/h3>\n<div class=\"group w-full text-gray-800 dark:text-gray-100 border-b border-black\/10 dark:border-gray-900\/50 bg-gray-50 dark:bg-[#444654]\">\n<div class=\"text-base gap-4 md:gap-6 md:max-w-2xl lg:max-w-2xl xl:max-w-3xl p-4 md:py-6 flex lg:px-0 m-auto\">\n<div class=\"relative flex w-[calc(100%-50px)] flex-col gap-1 md:gap-3 lg:w-[calc(100%-115px)]\">\n<div class=\"flex justify-between\">\n<div class=\"text-gray-400 flex self-end lg:self-center justify-center mt-2 gap-3 md:gap-4 lg:gap-1 lg:absolute lg:top-0 lg:translate-x-full lg:right-0 lg:mt-0 lg:pl-2 visible\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Question: Using integration, find th e area of the region bounded by y = m (m &gt; 0), x = 1, x = 2 and the x-axis. &nbsp; The correct answer is &#8211; To find the area of the region bounded by the lines y = m, x = 1, x = 2, and the [&hellip;]<\/p>\n","protected":false},"author":21842,"featured_media":132233,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12119],"tags":[],"class_list":{"0":"post-133898","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-quiz"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133898","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21842"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=133898"}],"version-history":[{"count":1,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133898\/revisions"}],"predecessor-version":[{"id":133900,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133898\/revisions\/133900"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/132233"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=133898"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=133898"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=133898"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}