Math 52 Final Exam Solutions
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چکیده
0 (r sin θ + z)r dz dr dθ (b) Let T be the solid ball of radius 1 centered at (2, 0, 0). Set up, but do not evaluate, a triple integral in spherical coordinates which computes the moment of inertia of T around the z-axis. Hint: First consider the change of variables u = x − 2, v = y, w = z. Solution. After the change of variables, the sphere takes the form u+v+w = 1, and the z-axis becomes the line (u, v) = (−2, 0). This means the distance from the z-axis is (u+ 2) + v, and therefore Iz = ∫ 2π
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