1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple integration but i cant get the answer

  1. Nov 23, 2009 #1
    [tex]\int xe^-^x^/^3dx[/tex] Integrating from 0 to infinity.

    So i did this by parts and end up with -3( [tex]\frac{x}{e^x^/^3}[/tex] + [tex]\frac{3}{e^x^/^3}[/tex] ) x is from 0 to infinity. So for [tex]\frac{x}{e^x^/^3}[/tex] if we sub in infinity it would be infinity/infinity? How do we do that?
     
  2. jcsd
  3. Nov 23, 2009 #2
    I am not really sure if it applies here but remember with horizontal asymptotes, if we were to have for example 3x/x, as x goes to infinity, it is a horizontal asymptote at 3 right?
     
  4. Nov 23, 2009 #3

    Mark44

    Staff: Mentor

    No, you don't substitute infinity - ever. Because infinity is one of the limits of integration, this is what is called an improper integral, so you need to use limits to evaluate it.
    [tex]\int_0^{\infty} xe^{-x/3}dx~=~\lim_{b \to \infty}\int_0^b xe^{-x/3}dx[/tex]

    Since you already have found the antiderivative, evaluate it at b and at 0, and take the limit as x approaches infinity. You will probably need to use L'Hopital's Rule for the x/e^(x/3) term.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook