Math Help - Convergent or Divergent!

1. Convergent or Divergent!

I have to determine if this integral is convergent or divergent! I know that i had to set the limit and everything, but i'm confused on how to start!

the integral of xe^-2x from 0 to infinity!

2. Question for you

Which tests do you know? (e.g. ratio test). Have you tried any of them?

3. I just know that you take the limit of that! I mean you set that the limit equal the integral and solve the integral, but I am confused here..

4. If this integral diverges

Then the limit doesn't exist. If it converges, then the limit exists so you should test first to see if the integral converges. Which test do you think you should try? (btw you may need to check for absolute convergence vs conditional convergence).

5. $
\int_0^{\infty}x e^{-2x}dx = \lim_{b \to \infty} \int_0^b x e^{-2x}dx
$

Integrate by parts, sub. in the limits then let $b \to \infty$.