Exam_exam_3_(3)

Exam_exam_3_(3) - D above the xy plane. Compute z . 4. (20...

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MATH 241 – Exam 3 – Boyle Wednesday April 15 1998 Show your work. Put a box around the result of a computation. 1. (20 points) Compute the following integral: Z 1 0 Z 1 y 2 sin( x 3 / 2 ) dxdy . (First draw the domain of integration. Then reverse the order of integration.) 2. (20 points) Compute the following integral: Z 1 0 Z 2 - y 2 y 1 x 2 + y 2 dxdy . (First draw the domain of integration. Then use appropriate coordinates.) 3. (25 points) Let D denote the portion of the unit ball (0 x 2 + y 2 + z 2 1) which lies in the ±rst octant ( x 0 , y 0 , z 0). Let ¯ z denote the average height of a point in
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Unformatted text preview: D above the xy plane. Compute z . 4. (20 points) Let T be the triangle with vertices (0 , 0) , (4 , 1) and (1 , 2). Let D be the triangle with vertices (0 , 0) , (1 , 0) and (0 , 1). Change variables to express the integral over T Z Z x 2 y dA as an integral over D . Do not evaluate the resulting integral, just set it up completely. 5. (20 points) Compute the volume of the region in the rst octant which is bounded by the coordinate planes and the plane x + y + z = 1....
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