- #1
TheMightyJ
- 8
- 0
Homework Statement
Basically, i have to find the solution to:
Int( x2 * exp (-(x-w)^2) , x= -infinity.. infinity)
Homework Equations
I realize this is connected to Gaussian Integration. So that if i have Int (exp(-x2), x=-infinity ... infinity) the answer is sqrt(Pi)
Also, i have read that there is a trick to solving such an integral.
you would consider F(a) = Int exp( - a * x^2) ( = sqrt(pi/a) ).
and then int dx x^2 exp(-x^2) = - F'(a) for a=1.
i understand this.
The Attempt at a Solution
Basically, the above is how i have attempted to work a way towards the solution, the trouble i am having is with a substitution i realize i must make at some point. at some point i must have x = x - w
But how do i implement this substitution??
This is my first post here, so hopefully that was somewhat clear and the relevant info is there. Thanks for any help.