What is the Integral of exp(-kx^2)?

[PhysForumID]

Hi there,
what's the integral over infinity of exp(-kx^2 )? the integral of exp(-x^2) is sqrt(pi)...
appreciate the help! I can't find the answer anywhere and can't work it out myself..

 

[HallsofIvy]

To integrate $\int_{-\infty}^\infty e^{-kx^2} dx$, let $u= x\sqrt{k}$ so that $du= dx \sqrt{k}$ and $dx= du/\sqrt{k}$.

Your integral becomes
$$\int_{-\infty}^\infty e^{-kx^2}dx= \frac{1}{\sqrt{k}}\int_{-\infty}^\infty e^{-u^2}du$$