Evaluate the integral by making the appropriate change in variables

[ptguard1]

∫∫9(x + y) e^(x2 − y2) dA, where R is the rectangle enclosed by the lines x−y=0, x−y=10, x+y=0, and x+y=5

Relevant Equations:

The Jacobian: ∂(x,y)/∂(u,v)

The attempt at a solution:

I began by making u=x+y and v=x^2-y^2

So, u=0 and u=5, but I don't know what to do with the x-y line segments.

 

[Dick]

Why not try u=x+y, v=x-y? Seems simpler to me.

 

[ptguard1]

Wow, I just realized how much more sense that makes. Thank you.