Mastering Integration: Proving the Integral of e-ax^2 and Solving for x2.e-ax^2

[henryc09]

Homework Statement

Given that:

The integral between infinity and -infinity of

e^{-ax^2} dx = \sqrt{\pi/a}

show that

The integral between 0 and infinity of

x².e^{-ax^2} dx = 1/4\sqrt{\pi/a^3}

Homework Equations

The Attempt at a Solution

don't really know where to start

 

[lurflurf]

integrate by parts