# [SOLVED] Cylindrical Coordinate Volume Integration

• Jul 17th 2009, 05:11 PM
1005
[SOLVED] Cylindrical Coordinate Volume Integration
9. Use polar coordinates to compute the volume of the region defined by 4 - x^2 - y^2 less or equal to z less than or equal to 10 - 4x^2 - 4y^2.

answer in book: 6pi
http://img149.imageshack.us/img149/3562/31957521.jpg
I got the root of 2 by setting the equations that bound z equal to eachother. It resulted in an equation for a circle equal to two. And to get the area of a circle, you have to do all 360 degrees, so I used 2pi. What's going wrong here?
• Jul 17th 2009, 05:54 PM
arbolis
In the triple integral, you have functions of \$\displaystyle x\$ and \$\displaystyle y\$ as upper limits. You have to translate them into polar coordinates.
• Jul 17th 2009, 05:58 PM
1005
Quote:

Originally Posted by arbolis
In the triple integral, you have functions of \$\displaystyle x\$ and \$\displaystyle y\$ as upper limits. You have to translate them into polar coordinates.

You can translate them before you put them in the limits for Z or after you've calculated the integral for Z. But while I checked your method through with mental math, I came across my rather awful error. I basically said -4r^2 -(-r^2) = -5r^2. But it should obviously equal -3r^2.

Problem solved. No one waste any more time here!