M2solns - Math 227.04 Solutions to Midterm Exam 2 1. 6 Z 2...

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Unformatted text preview: Math 227.04 Solutions to Midterm Exam 2 1. 6 Z 2 1 p x & 2 dx = lim a ! 2 + Z 6 a ( x & 2) & 1 = 2 dx = lim a ! 2 + 2 ( x & 2) 1 = 2 j 6 a = lim a ! 2 + f 2(6 & 2) 1 = 2 & 2( a & 2) 1 = 2 g = 4 & = 4 : 2. Let D be region in the &rst quadrant of the xy plane bounded by the curves y = x 2 and y = 0 and x = 2 : Suppose D is revolved around the line x = 2 . (a) Sketch the solid region. The sketches posted on a separate document. (b) Set up the volume integral using the disk/washer method. For each y between and 4 , the cross section is a disk of radius 2 & x where x = p y: Thus A ( y ) = & (2 & x ) 2 = & & 2 & p y 2 so V = Z 4 & (2 & p y ) 2 dy: (c) Set up the volume integral using the shell method. The shells are centered on the vertical line x = 2 . A typical shell has radius r = 2 & x and height h = x 2 and thickness dx: So V = Z 2 2 & (2 & x ) x 2 dx: (d) Compute the volume swept out using the your choice of the integrals in (b) or (c)....
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This note was uploaded on 10/16/2011 for the course MATH 227 taught by Professor Cheung during the Spring '09 term at S.F. State.

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M2solns - Math 227.04 Solutions to Midterm Exam 2 1. 6 Z 2...

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