Originally Posted by

**AllanCuz** This integral is bounded by

$\displaystyle x=0 $ and $\displaystyle x=y$

Also by

$\displaystyle y=0$ and $\displaystyle y=h$

If you graph the domain you will see we are bounded by the line y=x and the roof h. Of course, the line y=x is associated with $\displaystyle \frac{\theta}{4}$ and this would then be our start theta value. We are then bounded by x=0 or the y-axis.

$\displaystyle \frac{\theta}{4} \le \theta \le \frac{\theta}{2}$

We are not bounded by a cylinder, so we must find an equation of r that relates to theta. This can be done by looking at your domain and realising that

$\displaystyle sin ( \theta ) = \frac{H}{R}$

We then have

$\displaystyle R=Hcsc( \theta )$

Of course

$\displaystyle x=rcos(\theta)$

Why in gods name would you want to do this question in polar I have no idea. But this should be good