Double integral with transformations.

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

Re: Double integral with transformations.

Sorry for putting anyone out. I think I found the problem. Simple math errors have brought me undone.

First off I calculated the transformed points wrong. They should of been (-4,0), (-4,8), (4,0) and (4,8) which gives a nice square.

Also the integrand should of been .

So,

Thanks to anyone you read this. Please help with my other post about the TRIPLE INTEGRAL.