MTH 252 Integral Calculus Chapter 6 Integration Section 6 1 An Overview of the Area Problem Copyright 2005 by Ron Wallace all rights reserved Area Inscribed Regular Polygon 1 1 2 Atri r sin r cos r sin 2 2 4 r 2 2 n n 2 2 Apoly 2n Atri r sin 2 n Area Circle r Acircle Acircle lim Apoly n 2 sin r2 2 r2 n r2 2 2 lim lim 2 cos 2 r 1 poly 2 n 2 n n 2 n A n 2 r sin 2 n L H pital s Rule The Area Problem Given a continuous non negative function f x over an interval a b find the area bounded by f x the x axis x a x b A a1 a7 a4k x4k x3k 1f fx 3x k 1 k 1 7 a1 x0 a2 x1 x2 a3 a5 a4 x3 x4 a6 x5 a7 x6 x7 Example Approximate the area under f x sin x over 0 using 4 rectangles and left endpoints a2 0 4 a3 2 a4 3 4 a1 sin 0 0 4 a2 sin 0 555 4 4 a3 sin 0 7854 4 2 3 a4 sin 0 555 4 4 A 0 0 555 0 7854 0 555 1 8954 NOTE Actual area is 2 0
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