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Integration when given the exact value of an un-integratable function

  1. Mar 24, 2013 #1
    given that ∫ e^(-x^2) dx=√∏, calculate the exact value of ∫ e^-((x-a)^2)/c dx

    limits of integration for both are from negative infinity to infinity.

    I dont even know where to start on this one. I know how to integrate regular functions. How can I find the exact value for an integral I can't even integrate?

    Please Help
     
    Last edited: Mar 24, 2013
  2. jcsd
  3. Mar 24, 2013 #2

    Curious3141

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    Homework Helper

    The trick in these problems is to turn the new integral into the known one by a substitution.

    Can you think of a sub to turn that integral into [itex]\displaystyle \int_{-\infty}^{\infty} e^{-y^2}dy[/itex]?

    I'm using y to avoid confusion here. Keep in mind that in a definite integral, the actual variable of integration doesn't matter (it's a dummy).
     
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