The key is to use the change of variables theorem, such as when one changes between Cartesian and other (such as polar) coordinate systems.

Let us define new coordinates x',y' whose axes are rotated 45 degrees clockwise from the x,y axes. Then and . We can see that the Jacobian determinant , so dA=dxdy=dx'dy'. Note that in the x',y' coordinates, the region is the triangle with vertices (0,0), ( , ), and ( , )

Making the substitution, we see

Thus we have

You should be able to do that integral.

--Kevin C.