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.
(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 .
Can you proceed? Does this all make sense?