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

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Homework Help Overview

The problem involves integrating the function Exp[-(y^2)]*(y^2) with respect to y, with a specific request to express the result in terms of the error function.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use integration by parts but expresses uncertainty about its effectiveness. Some participants ask for clarification on the steps taken and the limits used in the integration process.

Discussion Status

The discussion is ongoing, with participants seeking to clarify the original poster's approach and offering hints related to the error function. There is no explicit consensus yet, but guidance has been provided to consider working backwards from the definition of the error function.

Contextual Notes

There may be constraints related to the requirement of expressing the answer in terms of the error function, which could influence the methods discussed.

garyng2001hk
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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
 
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I don't see why it wouldn't work. Can you show us exactly what you did?
 
What limits are you using?
 
garyng2001hk said:
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).
 

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