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Double Integral Choosing Change of Variable

  1. Dec 9, 2013 #1
    1. The problem statement, all variables and given/known data
    Evaluate the following integral with a change of variable of your choice.

    [tex]\int_0^{1} \int_y^{y+2} \sqrt{(x-y)}dxdy[/tex]

    3. The attempt at a solution

    I'm supposed to choose a u and v that will simplify the integral, but I have no idea how to even start this.

    I tried substituting u = x-y, but that doesn't even look like it would make my life simpler. If I did that, I'm not sure what I would choose for v.

    Any tips to push me in the right direction would be appreciated.
  2. jcsd
  3. Dec 9, 2013 #2


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    Education Advisor

    Have you tried to sketch the region that the integral is bounded over. If you do that you should be able to write four equations for the boundary lines, there should be two pairs that look the same (just shifted) and those two pairs will be your u and v. After that just use the jacobian and it becomes a simple integration problem.
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