Integrate Exp[-(y^2)]*(y^2) w.r.t. y

[garyng2001hk]

Homework Statement

Integrate Exp[-(y^2)]*(y^2) w.r.t. y

Homework Equations

The Attempt at a Solution

i need to express the answer in terms of error function

Error Function:

Erf(x) = 2/Sqrt[Pi] *Integrate Exp[-t^2] w.r.t. t, from 0 to x

My attemp is to use integration by part, seems doesn't work

 

[Char. Limit]

I don't see why it wouldn't work. Can you show us exactly what you did?

 

[hunt_mat]

What limits are you using?

 

[D H]

Error Function:

Erf(x) = 2/Sqrt[Pi] *Integrate Exp[-t^2] w.r.t. t, from 0 to x

Hint: Work backwards starting from erf(x).