$\displaystyle \int \int e^(-r(x-2y)^2) dxdy $

x =2u+v

y=u-v

The Jacobian is -3

I've substituted for x and y in the integral to get $\displaystyle \int \int -3e^r(3v)^2 dudv$

where r is a positive constant

But my problem lies with the limits, I have y is greater than or equal to 0 and x is less than or equal to 0, How do I change these for the integral and proceed as a result?

Thanks