Find centroid of region - triple integrals, please

[thaer_dude]

Homework Statement

Find the centroid [STRIKE]x[/STRIKE],[STRIKE]y[/STRIKE],[STRIKE]z[/STRIKE] of the region R cut out of the region 0<=z<=5sqrt(x²+y²) by the cylinder x²+y²=2x.

Homework Equations

x²+y² = r²
x= rcosθ
y= rsinθ

The Attempt at a Solution

Centroid [STRIKE]x[/STRIKE] being Mx/m I'm guessing

I've been working on this problem forever and I'm just not sure how to do it

I tried converting to polars and computing the following integral: $$\int_{-pi/2}^{pi/2}\int_0^{2cosθ}\int_0^{5r}$$ r dz dr dθ to get the integral that will be in the denominator (btw if you guys see the upper bound of the 2nd integral as 2cos952 it is 2cosθ)

and then for [STRIKE]x[/STRIKE] I replaced r by r^2cosθ and for [STRIKE]y[/STRIKE] replaced r by r^2sinθ and for [STRIKE]z[/STRIKE] replaced r by z*r

I'm not getting it right, and I'm going at this the completely wrong way or are my bounds incorrect or what? Please help, thanks so much :)

 

[Dick]

The integral and limits look ok to me. What are you getting for numbers?

 

[thaer_dude]

Thanks for the method confirmation, I tried it again, very carefully, and it worked! :)