Practice Exam 3 - lies above the cone z = p x 2 y 2 and...

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Warning: The following is a practice exam. Do not expect the actual exam to necessarily consist of the same or similar problems. 1. Evaluate R 4 0 R 2 p x e y 3 dy dx . 2. Evaluate RR D x 1 + y 2 dA ( x; y ) where D is the region in the °rst quadrant bounded by x 2 + y 2 = 3 . 3. Evaluate RRR E xz dV ( x; y; z ) where E is the solid tetrahedron with vertices (0 ; 0 ; 0) , (1 ; 1 ; 0) , (0 ; 1 ; 0) , and (0 ; 1 ; 1) . 4. Evaluate RRR E 1 p x 2 + y 2 + z 2 dV ( x; y; z ) where E is the solid region in the °rst octant which
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Unformatted text preview: lies above the cone z = p x 2 + y 2 and between the spheres x 2 + y 2 + z 2 = 9 and x 2 + y 2 + z 2 = 25 . 5. Use a change of variables to determine RR D x +3 y dA ( x;y ) where D is the parallelogram with vertices (1 ; 0) , ( & 1 ; 2) , ( & 2 ; 1) , (0 ; & 1) ....
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