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