Lets re-arrange, so in effect what we have is a plane and a cylinder of radius 1

To find our domain in the XY plane let these equal eachother such that

Now, what we are looking for is

We know our Z bounds (between the 2 equations we formatted). But what about X and Y. Well we might want to evaluate Y last because we have a function Y as our density.

So let us find when x=0

So now we know Y runs from 0 to the above. Find your X bounds, and which Z is bigger (either the cylinder or the plane) and put in your bounds accordingly. We are done!