# Gaussian integral

### From Conservapedia

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The **Gaussian integral** is the integral:

It has a value of . The value is needed to normalize the Normal distribution.

## Derivation

First look at the double integral

Separating it,

So, the double integral is merely the square of the Gaussian integral.

Now, do the double integral in polar co-ordinates. − *x*^{2} − *y*^{2} = − (*x*^{2} + *y*^{2}) = − *r*^{2} and *d**x**d**y* = *r**d**r**d*θ, so:

Substituting *z* = *r*^{2} into the integral,

Therefore,