# Integrate this integral from 0 to x of e^(-t^2)

1. Oct 15, 2004

### hytuoc

someone plz show me how to integrate this
integral from 0 to x of e^(-t^2)
Thanks

2. Oct 16, 2004

### Tide

Your integral has no simple closed form. However, that particular integral appears often enough to warrant its own special designation - it's call the "error function:"

$$erf(x) = \frac {2}{\sqrt \pi} \int_0^{x} e^{-t^2} dt$$

3. Oct 20, 2004

### quantitative

Don't you square it. Rename a variable. Then transform to polar co-ords. Then you get left with something along the lines of...

I^2 = 2pi.int^x_0 r.e^(-r^2)dr

which is easy.

Think it's also called the guassian integral or probability integral and must be one of the most common integrals, comes up all the time in stats etc...

4. Oct 20, 2004

### Galileo

Only when the limits of integration extend to infinity can we get a closed form expression by using that polar-coordinate trick.

What Tide means is that the antiderivative of $e^{-x^2}$ can't be expressed with elementary functions alone.