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Double integral transformation

  1. Mar 15, 2009 #1
    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, 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. jcsd
  3. Mar 15, 2009 #2
    What is 'SUP' supposed to stand for exactly? I'm assuming it's a mistake when you typed your formula...
     
  4. Mar 15, 2009 #3
    oh....that's funny that did that......it's just supposed to be superscripted......so int int (x^4-y^4)e^xy dA
     
  5. Mar 16, 2009 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

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