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Math Help - Improper Integral

  1. #1
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    Improper Integral

    Prove that \int_{-\infty}^{\infty} dx\: e^{-i x^2} = \int_{-\infty}^{\infty} e^{-ix^2} dx
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  2. #2
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    Re: Improper Integral

    Hey strammer.

    There is no work to do: they are both the same integral.

    Putting a dx on one side doesn't change the nature of the integral.
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  3. #3
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    Re: Improper Integral

    They apparently are not the same since d(xe^-ix^2) = e^-ix^2(1-2ix^2)dx
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  4. #4
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    Re: Improper Integral

    The post didn't have a bracket around the differential measure so I missed that.

    If the function is differentiable, then d(g(x)) becomes g'(x)dx and you can integrate as per normal.
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