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MATH 221 Midterm: MATH 221 KSU e2u07

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turquoisegnu128

15 Feb 2019

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Kansas State University

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The point value of each problem is given in the left-hand margin. (20) 1. a. ) Calculate the length of the curve y = ln x , 1 y . Find the area of the surface resulting from rotating the curve in part a. about the y-axis. ( the calculation in part a. can come in handy). (20) 2. Find the centroid of the region bounded by the curves y = x2 and y = 1 . Recall, for the region trapped between y = f (x) , y = g(x) , a x b , with uniform density = 1 we have mx = 1 a x(f (x) g(x)) dx. 2 r b a f (x)2 g(x)2 dx , my = r b page 2 of 6 (15) 3. Given the polar equation r = 2 cos(3 ) of the 3-leaved rose, nd the area inclosed by one loop. page 3 of 6 (15) 4.

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