Observe that and (we can't allow for -3 given the restriction on u). Thus, we see that .

Similarly, we see that and (again, we can't allow for due to the restriction on v). Thus we see that . We now have the limits for the transformed integral.

Next, we need to get x and y in terms of u and v and then find its Jacobian.

Observe that

(1) from the definition of v, and

(2) from the definition of u.

Substitute (1) into (2) to see that .

Multiply the corresponding sides of (1) and (2) together to get

Now find the Jacobian. I leave it for you to verify that .

Therefore,

Can you proceed? Does this all make sense?