- #1
Unredeemed
- 120
- 0
Homework Statement
Given that the integral from negative to positive infinity of e^(-(x^2))dx is equal to sqrt pi. Find the values of the integrals from negative to positive infinity of e^(-u*(x^2))dx and (x^2)*e^(-(x^2))dx.
Homework Equations
The Attempt at a Solution
I did the first one and got that it would be sqrt(pi/u).
But I honestly didn't know where to begin for the second. I drew graphs of y=e^(-(x^2)) and y=(x^2)*e^(-(x^2)), but it didn't help me massively.
I noticed that the graphs acted very similarly if -1/e>x or 1/e<x. But that might have just been how I'd drawn my graphs.
Can anyone help?
NB: I didn't know it was called the "Gauss Error Function" until i googled it, so this question assumes no knowledge of that.