Yes, that's all, now it's easy to check that $\displaystyle 8\,du\,dv=dx\,dy$ and your region is the circle $\displaystyle u^2+v^2\le1,$ so the common polar transformation will do the job.
Yes, that's all, now it's easy to check that $\displaystyle 8\,du\,dv=dx\,dy$ and your region is the circle $\displaystyle u^2+v^2\le1,$ so the common polar transformation will do the job.