Find-e-ax-2-dx-when-a-is-constant-without-changing-the-coordinate-

Question Number 214360 by shunmisaki007 last updated on 06/Dec/24

Find \underset{- \infty}{\int^{\infty}} e^{- {a x}^{2}} d x when a is constant without changing the coordinate .

Answered by mathmax last updated on 06/Dec/24

= 2 \int_{0}^{\infty} e^{- {a x}^{2}} d x {a > 0} \sqrt{a} x = t

= 2 \int_{0}^{\infty} e^{- t^{2}} \frac{d t}{\sqrt{a}} = \frac{2}{\sqrt{a}} \times \frac{\sqrt{π}}{2} = \frac{\sqrt{π}}{\sqrt{a}}

Facebook Tweet Pin