I have $$\iint_S (x^2-y^2)e^{(x+y)^2}\,dx\,dy $$ with restrictions $x+y\leq3$, $ xy\geq2$ and $y\leq x$
I think that with the variable changes $$u=x+y$$ and $$v=x-y$$
whose Jacobian is $2$ then I have the integral: $$\frac{1}{2}\iint_S u v e^{(u)^2} $$ My problem is when taking the limits of $u$ and $v$, someone can help me, i think the limits are
$$0\leq v \leq1 $$ and $$\sqrt{8+v^2}\leq u \leq 3 $$