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Math Help - cosine and exponential

  1. #1
    Junior Member
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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. #2
    Member Jason Bourne's Avatar
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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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