Multivariable Calculus : Triple Integral - Cylidrical Coordinates

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

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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

© BrainMass Inc. brainmass.com December 24, 2021, 4:55 pm ad1c9bdddf
https://brainmass.com/math/derivatives/multivariable-calculus-triple-integral-cylidrical-coordinates-16125

Solution Preview

We define
x=rcos(theta)
y=rsin(theta)
z=r
then the jacobian would be r. We must find

/ / /

| | |

| | | 1 dx dy ...

Solution Summary

A triple integral is calculated.

$2.49