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