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Calculus 3 Change of Variables: Jacobians

  1. Apr 30, 2009 #1
    1. The problem statement, all variables and given/known data
    Evaluate [tex]\int[/tex][tex]\int[/tex]e^xy dA, where R is the region enclosed by the curves: y/x=1/2 , y/x=2, xy=1, and xy=2.


    2. Relevant equations
    None?


    3. 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.
     
  2. jcsd
  3. May 1, 2009 #2

    HallsofIvy

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