Multiple integration + Centroid Help.

[numberonenacho]

Homework Statement

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

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

Please Help~! I am having some trouble.

 

[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.

 

[numberonenacho]

So when i evaluate it, I get -12pi rt6 as the answer.
Am I doing it wrong? I feel like I am 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~

 

[HallsofIvy]

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