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Solving an integral, what to substitute

  1. Jun 13, 2006 #1
    Hi

    Recently I found an integral which I can't solve, I don't know or can't guess how and what to substitute.

    [tex]\int_{\frac{3}{2}}^{2}(\frac{x-1}{3-2})^{\frac{1}{2}}dx[/tex]


    Please tell me what you would substitute and why you would do that
    Thanks


    ps:
    the solution isn't important to me, i want to understand and see how one can do that by oneself
     
  2. jcsd
  3. Jun 13, 2006 #2

    Hurkyl

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    I would start with the substitution 3 - 2 = 1.

    This is really an easy problem if you think about it at all -- think of an integral that you can do that looks similar, and make a substitution that makes this integral look more like that integral.
     
  4. Jun 13, 2006 #3
    oh, I actually noticed, that I made a typo, the denominator is wrong

    here is the right one:
    [tex]\int_{\frac{3}{2}}^{2}(\frac{x-1}{3-x})^{\frac{1}{2}}dx[/tex]

    still recomending the same substitution?
     
  5. Jun 13, 2006 #4

    Hurkyl

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    The two substitutions that came to mind would still be two of the first things I'd try... I suspect still that both will work.
     
  6. Jun 15, 2006 #5

    arildno

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    Arguably, the simplest substitution is to let the new variable equal the integrand.
     
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