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I have been asked to convert the following triple integral into spherical coordinates and then evaluate.

$\int^1_0 \int^\sqrt{1-x^2}_0 \int^\sqrt{1-x^2-y^2}_\sqrt{x^2+y^2} xy\, dz\, dy\, dx$

Unless I'm reading the bounds wrong they appear to be giving a description of shape that is best integrated in cylindrical in two parts.

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