Gaussian Integral

The Gaussian integral, otherwise known as the Euler-Poisson or probability integral, is the definite integral of the Gaussian function, $e^{x^2}$, over $(-\infty,\infty)$. This particular definite integral arises often when performing statistical calculations and when normalizing quantum mechanic wave functions. Here, the value of the Gaussian integral is derived through double integration in polar coordinates, namely shell integration.