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Finding limits of integration during a change of variables

  1. Mar 16, 2005 #1
    Hi. I have a problem with a question. Basically, I have an integral that goes from x=0 to x=1, and I'm supposed to make a change of variables like this:

    Let x = 1 - y^2.

    The problem I'm having is trying to find the limits of integration after the change of variables. Since y = +/- (x-1)^1/2, I have y = -1 or +1 for the lower limit. Am I supposed to just use either one? I'm so confused.
  2. jcsd
  3. Mar 16, 2005 #2


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    You need a bijection between the x's and the y's in this case.
    That is, you should choose
    EITHER [tex]y=\sqrt{1-x}[/tex]
    OR: [tex]y=-\sqrt{1-x}[/tex]
    Either one of them is okay; using both is wrong.
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