How to find the integral by changing the coordinates? Let R be the region in the first quadrant where
$$3 \geq y-x \geq 0$$
$$5 \geq xy \geq2$$
Compute
$$\int_A (x^2-y^2)\,dx\,dy.$$
I tried to use $ u= y-x, v= xy$ as my change of coordinates, but then I don't know how to solve it.
Can someone help me?

For the Jacobian, use this fact that:
$$\frac{\partial(x,y)}{\partial(u,v)}=\frac{1}{\frac{\partial(u,v)}{\partial(x,y)}}$$ provided $\frac{\partial(x,y)}{\partial(u,v)}\neq 0$.
