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Use polar coordinates to find the volume of the given solid:

Inside both the cylinder $x^2 + y^2 = 4$ and the ellipsoid $4x^2 + 4y^2 + z^2 = 64$

The limit of integration for the radius goes from 0 to 2 because the problem asks for the solid inside the cylinder? If it asked for the solid between the cylinder and ellipsoid it would be from 2 to 4?

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Provided that polar coordinates at XY plane, radius of your cylinder is 2, and your ellipsoid is 4. z coordinate will depend on r. –  0x2207 Dec 9 '12 at 15:32

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