# Find centroid of region - triple integrals, need help please!

## 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.

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 :)

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