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Math Help - Improper Integral

  1. #1
    Super Member redsoxfan325's Avatar
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    Improper Integral

    Prove that: \int_0^{\infty}\sin(x^2)\,dx = \sqrt{\frac{\pi}{8}}

    Further prove that: \int_0^{\infty}\sin(x^2)\,dx = \int_0^{\infty}\cos(x^2)\,dx

    Help on either one would be much appreciated.
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  2. #2
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  3. #3
    Super Member redsoxfan325's Avatar
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    Oh, so I imagine this is tough to prove. This isn't a homework problem or anything; I just found it by accident while using Maple and was curious why it was true.
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