f-e-x-2-dx-e-t-2-dt-1-2-pi-erf-t-Const-e-t-2-dt-pi-0-

Question Number 214366 by issac last updated on 06/Dec/24

f (α) = \int_{- \infty}^{\infty} e^{- α x^{2}} d x

\int e^{- α t^{2}} d t = \frac{1}{2} \sqrt{\frac{π}{α}} \cdot \erf (\sqrt{α} t) + Const

∴ \int_{- \infty}^{\infty} e^{- α t^{2}} d t = \sqrt{\frac{π}{α}}, α \in (0, \infty)