# Multivariable Calculus: Triple Integral - Cylindrical Coordinates

Not what you're looking for? Search our solutions OR ask your own Custom question.

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.

Â© BrainMass Inc. brainmass.com December 24, 2021, 4:55 pm ad1c9bdddfhttps://brainmass.com/math/integrals/multivariable-calculus-triple-integral-cylindrical-coordinates-16124

#### Solution Preview

We define

x=rcos(theta)

y=rsin(theta)

z=r

then the jacobian would be r. We must find

/ / /

| | |

| | | 1 dx ...

#### Solution Summary

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

$2.49