# Thread: Hey there! Unlimited integrals...

1. ## Hey there! Unlimited integrals...

Hey there.

I need help... I'm stuck in this question... I'm still not totally confident in LaTeX, so I'll try to insert the exported image from Mathtype.

I really hope someone can give a helping hand with this... Sometimes people are afraid to ask of help - this isn't such a time. : o) Any help would be appreciated! Notice the hints - they were supposed to make it a whole lot easier - I'm still struggling though.

Simon DK

2. This is what I get:

$u=\frac{x-\mu}{\sqrt{2}\sigma}$

$x=\sqrt{2}\sigma u + \mu$

$\int_{-\infty}^{\infty}x^2 f(x) dx=\int_{-\infty}^{\infty}(\sqrt{2}\sigma u + \mu)^2 \frac{1}{\sigma\sqrt\pi}e^{-u^2}\sqrt 2\sigma du$

$=\sqrt\frac{2}{\pi}\Big( 2\sigma^2\int_{-\infty}^{\infty}u^2 e^{-u^2}du + \mu^2\int_{-\infty}^{\infty} e^{-u^2}du\Big)$

If you're wondering what happened to the term with u times the exponential that "should" be there, it's zero because it's the integral of an odd function.

$=\sqrt\frac{2}{\pi}\Big( 2\sigma^2\frac{1}{2}\sqrt\pi + \mu^2\sqrt\pi\Big)=\sqrt 2 (\sigma^2+\mu^2)$

3. ## Thanks!

I see..! It was a great help. I'll try to search through the forums better next time... Have a nice weekend.

Simon DK