Are you familiar with jacobians? You should integrate using a double integral of the form:
Find the equations of the lines of the parallelogram so that you can find a transformation T from S in (u,v) to R (x,y) such that S is rectangular. Look in your book for some guidance, I'll help you find the region if you get stuck.
The transformation is a function
EDIT: Sorry, I worded that wrong and fixed it. I orignally mentioned a transformation T from S in (x,y) to R, however S is in the (u,v) plane NOT (x,y)... I hope I didn't cause any confusion...