Convergent or Divergent!

**littlesohi** · February 4th 2010, 01:55 PM

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!

**wonderboy1953** · February 4th 2010, 02:08 PM

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

**littlesohi** · February 4th 2010, 02:27 PM

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..

**wonderboy1953** · February 4th 2010, 02:38 PM

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).

**Danny** · February 4th 2010, 02:45 PM

$<br /> \int_0^{\infty}x e^{-2x}dx = \lim_{b \to \infty} \int_0^b x e^{-2x}dx<br />$

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

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