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Unformatted text preview: sphere of radius 2 centered at (0, 0, 2) which lies outside of the sphere of radius 3 centered at the origin. 5. (15 pts.) Find the area of the region enclosed in one leaf of the rose r = 2 cos2 q and which lies outside of the circle of radius 1 centered at the origin. 6. (15 pts.) Set up an integral expression for the surface area of z = 2 + ( xy ) 2 inside the cylinder ( x + 1) 2 + y 2 = 1. Express the integral in terms of polar coordinates. It is not necessary to evaluate the resulting integral. 7. (14 pts.) Use the transformation x = 3u + 2v, y = 2u 3v to evaluate ( x + 3 y ) dA R where R is the square bounded by the points (0, 0), (5, 1), (3, 2), and (2, 3). HINT: Take S = {(u, v)  0 = u = 1; 0 = v = 1}...
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This note was uploaded on 01/24/2011 for the course MATH 22 taught by Professor Brigham during the Winter '08 term at Missouri S&T.
 Winter '08
 BRIGHAM
 Integrals

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