Math13S09final_sol

Thus we get the following integral and change to

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Unformatted text preview: 2 and the region R is between the circle of radius 1 and 2 centered at the origin. Thus we get the following integral and change to polar coordinates to evaluate: 2π 2 θ =0 r =1 (1 + x2 + y 2 )dA = (a) R 2π (b) = 0 12 14 r+ r 2 4 2 2π dθ = 1 0 2π 2 θ =0 (1 + r 2 )r dr dθ = r =1 r + r 3 dr dθ 21 21 21π dθ = 2π · = 4 4 2 y z R 1 2 x z = 1 + x2 + y 2 R x y 5. We need the projection R, of the object into the yz -plane. So we need the projection of the intersection of y = 2x and x + z = 1 in the yz -pl...
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This note was uploaded on 01/20/2014 for the course MATH 13 taught by Professor Weiss during the Spring '07 term at Tufts.

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