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Multivariable Calculus: Triple Integral - Cylindrical Coordinates

Question: Solve by triple integration in cylindrical coordinates. Assume that each solid has unit density unless another density function is specified:

Find the volume of the region bounded above by the spherical surface x^2 + y^2 + z^2 = 2 and below by the paraboloid z = x^2 + y^2.

Solution Preview

We define
then the jacobian would be r. We must find

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Solution Summary

This solution is comprised of a detailed, step-wise response which shows how a triple integral is solved. All calculations are included.