hgfj - above by the plane z = 2. Set up the triple integral...

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MATH 241H - EXAM 3 - November 1 , 2004 No calculators. Show your work. [15] 1. Evaluate R 1 0 R 1 y x 2 cos( xy ) dxdy . (Hint: change the order of integration.) [20] 2. Let R be the region in the xy -plane bounded by the positive x -axis and the spiral r = θ, 0 θ 2 π . (a) Sketch the region R . (b) Find the area of R . [20] 3. Evaluate R R R D 1 x 2 + y 2 dV where D is the solid region bounded by the paraboloids z = 5 - x 2 - y 2 and z = 1 + x 2 + y 2 . [25] 4. Let D be the solid region bounded below by the cone z = p x 2 + y 2 and bounded
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Unformatted text preview: above by the plane z = 2. Set up the triple integral Z Z Z D ( x 2 + y 2 + z ) dV as an iterated integral in (a) rectangular coordinates (b) cylindrical coordinates (c) spherical coordinates. Do not evaluate the integral. [20] 5. Let R be the region bounded by the lines 2 x + y = 1 , 2 x + y = 4 , x-y = 1 , x-y =-1. Evaluate Z Z R (2 x + y ) e x-y dA by using a suitable change of variables....
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