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Thread: cosine and exponential

  1. October 13th 2008, 09:00 PM #1
    graticcio
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    Question cosine and exponential

    what is the answer to

    \frac{1}{\sqrt{2\pi t}} \int_{-\infty}^{\infty} cos(ax) e^{-x^2/2t} dx
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  2. October 14th 2008, 07:07 AM #2
    Jason Bourne
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    Quote Originally Posted by graticcio View Post
    what is the answer to

    \frac{1}{\sqrt{2\pi t}} \int_{-\infty}^{\infty} cos(ax) e^{-x^2/2t} dx
    I'm not 100% sure about this but from the normal distribution:

    \int^\infty_{-\infty} e^{\frac{{-x^2}}{2}} dx = \sqrt{2\pi}

    I think if you carry out integration by parts using this you should find that the integral is equal to zero. Does this help?
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