4 (10 points). Evaluate the double integral fR f (as, y)dA, where R = [0, 2] X [0, 2] and
(93,31) 6 [0, 1) X [0,11
(90,11) 6 [1,2] x [0,1]
(any) 6 [0,2] x (1,2]
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Test #3 (Math 247) (Fall 2012)
Do all problems and give the process of your solution.
1 (16 points). Find the volume of the solid under the surface 2 = ((172 + 1112)?2 and
above the disk D = {(22, y)| 3:2 + y2 S 1}.
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5 (16 points). Compute the work done by the force eld F(9:, y, z) = xi - zj +yk from
(0, 0, W, , along the curve C: a: = 2t, y 2 3t and z = t2. \7/ lb;
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Quiz #7 Math 247 Fall 2012
1. Mass is distributed over the triangular region bounded by the line a: z 0, y = 0
and a: + y = 1 with density p(:c, y) = x + y. Find the center of the mass.
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Test #1 (Math 247) Fall 2012
Do all problems and give the process of your solution.
1. (15 points) Identify the surface (as specic as you can) represented by the equation
2 2 2 _ = k i W.)
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