{"id":13997,"date":"2023-05-02T10:00:05","date_gmt":"2023-05-02T04:30:05","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=13997"},"modified":"2023-05-03T09:44:31","modified_gmt":"2023-05-03T04:14:31","slug":"area-under-curve","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/area-under-curve\/","title":{"rendered":"Area Under a Curve"},"content":{"rendered":"
If the curve is symmetrical about a co-ordinate axis (or a line or origin), then we find the area of one symmetrical portion and multiply it by the number of symmetrical portions to get the required area.<\/p>\n
If a plane curve is revolved about some axis in the plane of the curve, then the body so generated is known as solid of revolution. The surface generated by the perimeter of the curve is known as surface of revolution and the volume generated by the area is called volume of revolution.
\nFor example, a right angled triangle when revolved about one of its sides (forming the right angle) generates a right circular cones.<\/p>\n
(1) Volumes of solids of revolution<\/strong><\/p>\n (2) Area of surfaces of revolution<\/strong><\/p>\n (3) Volume and surface of the frustum of a cone<\/strong> (4) Volume and surface of the frustum of a sphere<\/strong><\/p>\n Let the thickness of the frustum of sphere is k and radii of the circular ends of the frustum are r1<\/sub>\u00a0and r2<\/sub>, then<\/p>\n 1.<\/strong> Area Under a Curve Area of bounded regions The area bounded by a cartesian curve y = f(x), x-axis and ordinates x = a and x = b is given by If the curve y = f(x) lies below x-axis, then the area bounded by the curve y = f(x)\u00a0the x-axis and the ordinates x […]<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[5315,5313,5319,5312,5322,5316,5314,5320,5321,5317,5318],"yoast_head":"\n\n
\n<\/li>\n\n
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\nwhere t1<\/sub> and t2<\/sub> are the values of the parameter corresponding to x = a and x = b.<\/li>\n<\/ol>\n
\nIf r1<\/sub>, r2<\/sub>\u00a0be the radii of the circular ends and k is the distance between centres of circular ends and l be the slant height, then<\/p>\n\n
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Area Under a Curve Problems with Solutions<\/h3>\n
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\nSolution:<\/strong>
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\nSolution:<\/strong>
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