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Test3Review

# Test3Review - Test 3 Review 1 Evaluate the following...

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Test 3 Review 1. Evaluate the following integrals (you may need to switch order of integration): (a) Z π 0 Z x 0 x sin y dy dx (b) Z 3 0 Z 1 x/ 3 e y 3 dy dx (c) Z 1 - 1 Z 1 - y 2 - 1 - y 2 ( x 2 + y 2 ) dy dx (d) Z 2 0 Z 1 - ( x - 1) 2 0 x + y x 2 + y 2 dy dx (e) Z 1 0 Z 2 - x 0 Z 2 - x - y 0 dz dy dx (f) Z 1 - 1 Z 1 - y 2 0 Z x 0 ( x 2 + y 2 ) dz dx dy 2. Set up integrals to integrate over the following regions: (a) the solid whose base is the region in the xy -plane that is bounded by the parabola y = 4 - x 2 and the line y = 3 x , while the top of the solid is bounded by the plane z = x + 4. (b) the (2-dimensional) region bounded by y = e x and the lines y = 0 ,x = 0 ,x = ln 2. (c) the (2-dimensional) region bounded by the parabolas x = y 2 - 1 and x = 2 y 2 - 2. (d) the region cut from the ﬁrst quadrant by the cardiod r = 1 + sin θ . (e) the tetrahedron cut from the ﬁrst octant by the plane 6 x + 3 y + 2 z = 6. (f) the region bounded by the paraboloids z = 8 - x 2 - y 2 and z = x 2 + y 2 . (g) the region bounded by the cylinder z = y 2 , and the planes z = 0 ,x = 0 ,x = 1 ,y = - 1 ,y = 1. (h) (using cyclindrical coordinates) region bounded by
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