# Gaussian Integral

$\displaystyle \int_{-\infty}^\infty e^{-x^2} \rd x = \sqrt \pi$
 $\displaystyle \int_{-\infty}^\infty e^{-x^2} \rd x$ $=$ $\displaystyle 2 \int_0^\infty e^{-x^2} \rd x$ Definite Integral of Even Function $\displaystyle$ $=$ $\displaystyle \frac {2 \sqrt \pi} 2$ Integral to Infinity of Exponential of -t^2 $\displaystyle$ $=$ $\displaystyle \sqrt \pi$
$\blacksquare$