Integrating challenge I am having

[terp.asessed]

Hi, I am doing an exercise practice samples for the upcoming quiz, and stumbled across two questions I'm having trouble solving...

First question is to integrate integral e^-x2 dx ...where the solution is equal to pi^1/2

Also...

As for the second question (of a different equation) how can one solve for the result when I integrated an equation (another example) and got a x*e^-x2 = ?, where x = -infinite to x = infinite? The answer is 0, but I don't know how to get there.

If anyone could explain, I'd appreciate it!

 

[Simon Bridge]

In the first problem:$$\int e^{-x^2}\;dx$$... where the solution is $\sqrt{\pi}$ ?
Did you miss out the limits of the integration?
Over the entire number line, this is called "the Gaussian Integral".
See: http://en.wikipedia.org/wiki/Gaussian_integral

For the other one: $$\int_{-\infty}^\infty xe^{-x^2}\; dx = 0 $$ ...you should be able to tell that is true by looking at the symmetry, but you may prefer to use a substitution.
What have you tried?

 

[terp.asessed]

Hello, thank you for hints--I just realized I made a mistake in my substitution. I got 0--and yes, since the area under the one curve is + and the other -, altogether, they become 0.