# Thread: Improper Integral Evaluation

1. ## Improper Integral Evaluation

Does anyone know how to find the integral of abs(x)e^((-x)^2)dx from negative infinity to infinity? I can't quite figure out how to do this...

2. See attachment

3. hmmm... strange it's not indicative of anything we have been working on...

4. No you're all right, that's not the same problem at all, which is:

$\int_{-\infty}^{\infty} |x| e^{-x^2} dx$

(sorry but I don't believe $e^{(-x)^2}$ because that won't converge.)

You can split it into two bits: one for x positive, one for x negative. Let's do

$\int_0^{\infty} x e^{-x^2} dx$

Put $z = x^2$ and that gives you an easy integral in $e^z$.

Now do the same for

$\int_{-\infty}^0 -x e^{-x^2} dx$

and add them together.

If I'm wrong about it NOT being $e^{(-x)^2}$ then it could be the answer is supposed to be zero because one half equals minus the other half ...?

5. e^(-x^2) is always positive

Int e^(-x^2) from -inf to pos inf is sqrt(pi)-- this is one of those well known results - the Gaussian Integral See Gaussian integral - Wikipedia, the free encyclopedia

however i read the original pblm here incorrectly --didn't see the abs|x| out front so for your problem it works out to 1