$x=4$

The formula $\frac{1}{\sqrt{2\pi}}\int_{-\infty}^\infty e^{-x^2/2}dx = 1$ is one of the most important improper integral calculations in mathematics. It is usually first met in probability theory, where it leads to the normal distribution.There are *many* proofs of this basic result. We will see how many I can get through before time runs out.