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## Homework Statement

Prove that the integral of the Guassian Distribution converges to 1:

[tex]\int_{- \infty}^{\infty} \frac{1}{\sigma \sqrt{2 \pi}} e^{- \frac{(x- \mu )^2}{2 \sigma ^2}} dx = 1[/tex]

## Homework Equations

none

## The Attempt at a Solution

So I get that I can pull the constants out for the first step, but I have no clue where to go from there. I looked online for a solution and read about having to convert it to polar or something to solve it so now I am really confused. I thought it might work with a simple substitution, one that I just can't think of.

Any help greatly appreciated.

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