# Math Help - cosine and exponential

1. ## cosine and exponential

what is the answer to

$\frac{1}{\sqrt{2\pi t}} \int_{-\infty}^{\infty} cos(ax) e^{-x^2/2t} dx$

2. Originally Posted by graticcio
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?