# Need help trying to integrate a messy function

1. Feb 12, 2012

### insane0hflex

1. The problem statement, all variables and given/known data
Evaulate the following integral:
2*integral from r-b to r of h(x-r+b)b*sqrt(r2-x2) dx
or a picture
http://imgur.com/n2PUN

2. Relevant equations

3. The attempt at a solution

Tried setting u = r^2-x^2, lost after a couple more steps. Nothing seems to cancel out smoothly. For the record, Im in Calc II, and have not learned integral by parts or trig sub.
Heres a webpage I got the integral from http://mathworld.wolfram.com/CylindricalWedge.html

Last edited: Feb 12, 2012
2. Feb 12, 2012

### δοτ

I assume r, b, and h are constants. If so, split the integral into
$2\displaystyle\int\limits_{r-b}^r \dfrac{hx}{b} \sqrt{r^2 - x^2} dx + 2\int\limits_{r-b}^r \frac{h(b-r)}{b} \sqrt{r^2 - x^2} dx$

Then the first can be done with the substitution you've tried already, and the second will require a trig substitution.

3. Feb 12, 2012

### insane0hflex

Thank you, worked it out and will ask the professor tomorrow. Thanks for your help!