integral of exp(-x) * x^n

• Dec 11th 2012, 09:17 PM
Kiki
integral of exp(-x) * x^n
integration from 0 to infinity, of exp(-x) * x^n with respect to x.

• Dec 12th 2012, 12:41 AM
MarkFL
Re: integral of exp(-x) * x^n
Define $f(n)\equiv\int_0^{\infty}x^ne^{-x}\,dx$ and use integration by parts to show that:

$f(n)=nf(n-1)$ and hence:

$f(n)=n!$
• Dec 12th 2012, 12:44 AM
mathlover10
Re: integral of exp(-x) * x^n
by the way how do you post in integral typeset like that?
• Dec 12th 2012, 12:58 AM
MarkFL
Re: integral of exp(-x) * x^n
It is done using $\LaTeX$. There is a forum here dedicated to its usage, and there are many good tutorials online too.