Double Integral: trouble manipulating algebra

[glog]

Homework Statement

$$\int\int e^(^x^2^+^y^2^) dA$$ where D is the region bounded by y = sqrt(1-x^2) and y = |x|.

Homework Equations

The Attempt at a Solution

Obviously I can draw this region out and see what it looks like, and I will have to split the integral into two for negative and positive x, however, I set up my ranges:

x <= y <= sqrt (1-x^2) and 0 <= x <= 1/sqrt(2) for the first quadrant, and I still do not know how to integrate the function e^(x^2+y^2) in a 'nice' way. I even tried reversing the variables, but it didn't make a difference since the function is symmetric in x and y.

 

[glog]

Nevermind... this needs to be done with polar co-ordinates.

Thanks
-glog