Originally Posted by

**Bud** Hi there,

I found this line in a book which I would like to understand:

$\displaystyle K \int^{+\infty}_{-\infty}e^{-ax^{2}}dx = K \left(\frac{\pi}{a}\right)^{\frac{1}{2}}$

I tried to follow this step, but I did not succeed. I tried to calculated the limits after I determined the integral using l'hopital's rule:

$\displaystyle K \int^{+\infty}_{-\infty}e^{-ax^{2}}dx = \left[ -\frac{1}{2ax}e^{-ax^{2}} \right]^{+\inf}_{-\inf}$ Mr F says: This is wrong. If you differentiate the anti-derivative you found, it is clear that you do not get the integrand. In fact, no anti-derivative exists in closed form using elementary functions.

Does somebody know how to handle this?

Thanks in advance

Cheers

Bud