Question Number 208632 by necx122 last updated on 19/Jun/24
$$\int{e}^{−{x}^{\mathrm{2}} } {dx} \\ $$$${could}\:{this}\:{be}\:{integrated}\:{by}\:{part}?\:{What} \\ $$$${approach}\:{would}\:{most}\:{likely}\:{be}\:{suitable} \\ $$$${for}\:{this}\:{integral}? \\ $$$$ \\ $$
Commented by Tinku Tara last updated on 20/Jun/24
https://en.m.wikipedia.org/wiki/Gaussian_integral
Answered by Berbere last updated on 19/Jun/24
$$\frac{\mathrm{2}}{\:\sqrt{\pi}}\int_{\mathrm{0}} ^{{x}} {e}^{−{t}^{\mathrm{2}} } {dt}={erf}\left({x}\right) \\ $$