FinalReview - MATH 32B: FINAL EXAM REVIEW PROBLEMS Problem...

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Unformatted text preview: MATH 32B: FINAL EXAM REVIEW PROBLEMS Problem 1. Compute RR R f ( x,y ) dA , where f ( x,y ) = p 4- y 2 +4 and R = [- 1 , 2] [- 2 , 2] by identifying this integral of the volume of a solid. Problem 2. Evaluate: (a) R 1- 1 R 2 y 1+ x 2 dy dx (b) RR R 6 xy ( x + y 2 ) dA , where R is the rectangle with vertices (- 2 , 3) , (1 , 3) , (- 2 , 6) , (1 , 6) (c) RR R xye x 2 y dA , where R = [0 , 1] [0 , 2]. Problem 3. Evaluate: (a) R 1 R 3 3 y e x 2 dxdy (b) RR R | x | dA , where R is the region where | x | 1 , | y | 1, and | x | + | y | 1. (c) R 8 R 2 3 y e x 4 dxdy . Problem 4. Suppose the volume of the solid in the first octant bounded by the surface ax + 3 y + 2 z = 12 is equal to 4, where a > 0. Find a . Problem 5. The area enclosed by one loop of the curve given in polar coordinates by r = c cos(2 ) is equal to 1, with c > 0. Find c . Problem 6. Evaluate R x 2 e- x 2 dx using the fact that R - e- x 2 = ....
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This note was uploaded on 06/03/2011 for the course PHYSICS 1B 1b taught by Professor Corbin during the Winter '10 term at UCLA.

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FinalReview - MATH 32B: FINAL EXAM REVIEW PROBLEMS Problem...

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