I need help in determine the limits of the double integrals where I had to use transformations.

The double integral is where R is a parallelogram with vertices (-1,3), (1,-3), (3,-1) and (1,5).

The transformations were given as: , .

Using the transformation equations of and (solving simultaneoulsy from above), the points in the transformed plane become (-4,-2), (-4,-6), (4,10) and (4,6).

I calculated the Jacobian as and the integrand becomes .

So,

where r is the region in the transformed plane.

Could someone please help to me with what the * * limits of the inner integral would be and correct any errors I have made in getting this far?

Thanks in advance,

Tammy