The parabolas divide the plane into 7 regions, of which only one is bounded. Let this region be A. Find a change of variables such that the first two parabolas become u=0 and v=0. Evaluate the double integral .
I should clarify - I can find the Jacobian factor and the "new" integrand in terms of u and v. The only problem is that I don't know what the region should be (ie the limits of the u and v integrals). In fact I'm not too sure how to desribe the region on x and y coordinates (ie I'm not sure what the limit of the integrals would have been before the change of variables anyway).
A way to see it better would to graph the 3 curves. Check out the region 0<y<1 , -2<x<2.
So the integration in that region would be, in x and y coordinates:
Darnit! For some reason it wont let me edit my own posts. My integrals are slightly wrong, they should be instead of
[Fixed. -K.]