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 and this would then be our start theta value. We are then bounded by x=0 or the y-axis.
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
We then have
Why in gods name would you want to do this question in polar I have no idea. But this should be good