(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that [tex]\int_{0}^{\infty}x^{2}e^{-x^{2}}dx = \frac{1}{2}\int_{0}^{\infty}e^{-x^{2}}dx.[/tex]

2. Relevant equations

None.

3. The attempt at a solution

I used substitution:

[tex]t = x^{2}[/tex]

[tex]dx = \frac{dt}{2x}[/tex]

[tex]\frac{1}{2}\int_{0}^{\infty}\sqrt{t}e^{-t}dx[/tex]

Then tried using integration by parts but then I didnt get an answer and got stuck.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Improper integral x^(2) * e^(-x^2)

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