# Multivariable Calculus : Triple Integral - Cylidrical Coordinates

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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

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##### Solution Summary

A triple integral is calculated.

##### Solution Preview

We define

x=rcos(theta)

y=rsin(theta)

z=r

then the jacobian would be r. We must find

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| | | 1 dx dy ...

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