Calculus 3 Change of Variables: Jacobians

[Wargy]

Homework Statement

Evaluate $$\int$$$$\int$$e^xy dA, where R is the region enclosed by the curves: y/x=1/2 , y/x=2, xy=1, and xy=2.

Homework Equations

None?

The Attempt at a Solution

I have the region graphed and I'm currently working on acquiring the change of variables functions in x and y. I have attempted to solve the system of equations with u=y/x and v=xy to obtain these but I'm having some trouble. If I could be pointed in the right direction I would be greatly appreciative! Thanks.

 

[HallsofIvy]

You have u= y/x and v= xy so y= xu. Substitute that into v= xy: v= x²u. Now solve for x.