# Multiple integration + Centroid Help.

1. Nov 24, 2007

### numberonenacho

1. The problem statement, all variables and given/known data
Find the volume bounded by sphere rho = rt. 6 and the paraboloid z = x^2 + y^2
and locate the centroid of this region

The attempt at a solution

http://www.mathhelpforum.com/math-help/latex2/img/4deb41286077aabd94b30802f0e6a68a-1.gif [Broken]

So Thats the integral that I made for this problem, but I'm having trouble integrating it. the rdr throws it off.

Last edited by a moderator: May 3, 2017
2. Nov 24, 2007

### Kummer

You first integrate with z, that gives you rz in the inside. Using Fubini you get (meaning evaluate the integral) $$r\sqrt{6-r^2} - r(r^2)$$ and now continue with r and theta.

3. Nov 24, 2007

### numberonenacho

So when i evaluate it, I get -12pi rt6 as the answer.
Am I doing it wrong? I feel like im not doing right. If you could, could I see how someone would do a problem like this? Evaluating integrals is a little confusing for me.

And then I need lots of help on the centroid part as well. Thanks~

4. Nov 25, 2007

### HallsofIvy

Staff Emeritus
Why don't you show us what you did and we can comment on it.