# Homework Help: Need help with infinite integral

1. Jan 6, 2008

### Pollywoggy

I found an example on p. 14 of Quantum Mechanics Demystified (McMahon) which I don't understand. The part I do not understand is how they got the part on the right side of the equal sign from the part on the left.

$$\int^\infty_0 e^{-2x^2}\,dx =\sqrt{\pi/8}$$

I looked at several books but could not find an explanation that applies here.

thanks

2. Jan 7, 2008

### Rainbow Child

It is based on

$$I=\int_0^{+\infty}e^{-u^2}\,d\,u=\frac{\sqrt{\pi}}{2}$$

which is proved by several methods. If you know double integrals there is an easy way to show it.

3. Jan 7, 2008

### Pollywoggy

Thanks, you have answered my question. I saw a *similar* equation in another book explained with double integrals and it was stated that the equation could not be solved by the methods shown up to that point.

4. Jan 7, 2008

### Kaan

It will basically work if you know how to switch to polar cordinates.