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practice31answers - Practice Exam 1 Solutions Most of the...

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Practice Exam 1 Solutions Most of the multiple choice answers are (A); the following are typos: The answer to 2 is 8 π , which is (C). The lamina in 3 should be Ω = { ( x, y ) : x 2 + y 2 π 2 , y 0 } (NOT x 2 + y 2 = π ). The answer to this problem is (A). In 7, the volume of is written twice; otherwise it is fine, and the answer is (A). 8: The integrand should be x - 2 y . The answer to this problem is -16, which is not listed as a choice. (Note: Even if you assume the function is x + 2 y the answer you got is still not listed as one of the choices.) In 9, the transformation should have y = 2 v (NOT y = 3 v ) and the answer is 0, which is not listed as one of the choices. 10: The answer is 30, which is not listed. 13. Evaluate the interated integral R 3 0 R 0 - 9 - y 2 x 2 y dx dy by converting to polar coordinates. First, we are integrating over the region D = { ( x, y ) : - p 9 - y 2 x 0 , 0 y 3 } which corresponds to the quater of the circle of radius 3 in the second quadrent. Therefore Z 3 0 Z 0 - 9 - y 2 x 2 y dx dy = ZZ D x 2 y dA = Z 3 0 Z
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