# Double integral transformation

1. Mar 15, 2009

### vampireyal

1. The problem statement, all variables and given/known data
evaluate the integral $$\int\int(x^4-y^4)e^{xy}dA$$

where R is the region bounded by xy=1, xy=2, x2-y2=1, and x2-y2=4

2. Relevant equations

3. The attempt at a solution

This is my first time on the forum, so forgive me if there are mistakes in this post. I am trying to find the transformation equations in order to convert the xy-plane equations to a uv-plane. Judging by the boundary equations, I let u=xy and v=x2-y2.

When I evaluate the xy equations using the transformation equations I get u=1, v=4, u=2, and v=1. which makes a square on the uv plane. I am not sure if I did this correctly though.

The next part of the problem asks to calculate the Jacobian, but I am not sure of how to calculate the partial derivatives based off my transformation equations. I can't seem to get x and y in terms of u and v, which makes me think that my transformation equations are wrong.

Any help is appreciated. Thank you.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: Mar 16, 2009
2. Mar 15, 2009

### Fragment

What is 'SUP' supposed to stand for exactly? I'm assuming it's a mistake when you typed your formula...

3. Mar 15, 2009

### vampireyal

oh....that's funny that did that......it's just supposed to be superscripted......so int int (x^4-y^4)e^xy dA

4. Mar 16, 2009

### HallsofIvy

Staff Emeritus
Don't use "sup" inside LaTex. Use "^" instead.