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MTH 162 Midterm: MTH 162 University of Rochester Fall 11Exam2 Solutions

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turquoisegnu128

31 Jan 2019

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University of Rochester

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November 10, 2011: (20 points) (a) compute the area of surface of revolution obtained by rotating the curve y = x3, for. 0 x 1, about the x-axis. (b) do the same for the curve y = |x|, for 1 x 1. Solution: (a) yp1 + (dy/dx)2 dx x3 1 + 9x4 dx. U du (u = 1 + 9x4, du = 36x3 dx) 27(cid:16)10 10 1(cid:17) (b) we have so dy dx. =( 1 for x < 0 for x > 0. Do not use the picture to justify your answer! (b) the curve passes through the origin twice. Solution: (a) we have dy dx dy/dt dx/dt. Cos( t) and the tangent line is horizontal when this derivative is 0, namely when t = 1. The corresponding cartesian point is (sin( ( 1)), ( 1)2 + 2( 1)) = (0, 1). (b) the curve passes through the origin at t = 0 and t = 2.

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