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Homework Help: Evaluate the integral by making the appropriate change in variables

  1. Jul 17, 2012 #1
    ∫∫9(x + y) e^(x2 − y2) dA, where R is the rectangle enclosed by the lines x−y=0, x−y=10, x+y=0, and x+y=5

    Relevant Equations:

    The Jacobian: ∂(x,y)/∂(u,v)

    The attempt at a solution:

    I began by making u=x+y and v=x^2-y^2

    So, u=0 and u=5, but I don't know what to do with the x-y line segments.
  2. jcsd
  3. Jul 17, 2012 #2


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    Science Advisor
    Homework Helper

    Why not try u=x+y, v=x-y? Seems simpler to me.
  4. Jul 17, 2012 #3
    Wow, I just realized how much more sense that makes. Thank you.
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