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**1. The problem statement, all variables and given/known data**

evaluate the integral [tex]\int\int(x^4-y^4)e^{xy}dA[/tex]

where R is the region bounded by xy=1, xy=2, x

^{2}-y

^{2}=1, and x

^{2}-y

^{2}=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=x

^{2}-y

^{2}.

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**

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