# Math Help - inverse Fourier transform

1. ## inverse Fourier transform

How does one show that the inverse Fourier transform of e^-a|y|, a>0 is

(a/pi)*1/(x^2+a^2)

thanks!

2. Have you considered the definition of the Transform?

3. Yes, but I'm confused about how to integrate e^-a|y|*e^-iyx to get that answer

4. I would probably use the equation

$|y|=\begin{cases}y,\quad &y\ge 0\\ -y,\quad &y<0\end{cases},$

and then split up your integral into two pieces depending on which of the two cases is applicable.