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 first 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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