Gausian Integrals... How do you do this one?

May 2010
13
0
Trying to solve this Gaussian integral, any help please?

\(\displaystyle
\int^{\infty}_{0} x e^{-x^2} dx
\)

Thanks
Chris
 
Nov 2008
1,458
646
France
Hi

What is the derivative of \(\displaystyle e^{-x^2}\) ?
 
May 2010
13
0
I believe the intergration of

\(\displaystyle e^(-x^2)\)

with limits 0 and \(\displaystyle \infty\)

is

\(\displaystyle \int^{\infty}_{0} e^{-x^2} = \sqrt{\pi}\)
 
Nov 2008
1,458
646
France
I was not asking for the integration of \(\displaystyle e^{-x^2}\) but its derivative (Wink)
 
May 2010
13
0
\(\displaystyle -2xe^{-x^2}\) ??

Am i missing something here?
 
Nov 2008
1,458
646
France
The derivative of \(\displaystyle e^{-x^2}\) is \(\displaystyle -2xe^{-x^2}\)

Therefore an antiderivative of \(\displaystyle -2xe^{-x^2}\) is \(\displaystyle e^{-x^2}\)

And an antiderivative of \(\displaystyle xe^{-x^2}\) is \(\displaystyle -\frac12 e^{-x^2}\)
 
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