Let E be the solid ellipsoid E = {(x, y, z)

Chapter , Problem 12

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Let E be the solid ellipsoid E = {(x, y, z) | (x/a)+ ( y/b) + (z/c) 1}, where a > 0, b > 0,and c > 0. Evaluate xyz dx dy dz (a) over the whole ellipsoid; and (b) over that part of it in the first quadrant: x x 0, y 0, and z 0, x a + y b + z c 1.

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