1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Integration by Parts separately

  1. Jan 19, 2010 #1
    1. The problem statement, all variables and given/known data

    Integrate: [tex]-\frac{2}{\theta} \int^{\infty}_0 y e^{-2y/\theta} dy + \frac{2}{\theta} \int^{\infty}_0 y e^{-y/\theta}dy[/tex]

    2. Relevant equations

    3. The attempt at a solution

    Let u = y/theta; y=u*theta; dy = du*theta, which becomes

    [tex]-2 \int^{\infty}_0 u \theta e^{-2u} du + 2\int^{\infty}_0 u \theta e^{-u}du[/tex]

    Doing each integral seperately and then adding them up:

    [tex]-2 \int^{\infty}_0 u \theta e^{-2u} du = u\theta e^{-2u} |^{\infty}_0 - 2 \theta \int^{\infty}_0 e^{-2u} du = \theta e^{-2u} |^{\infty}_0 = - \theta[/tex]

    [tex]2\int^{\infty}_0 u \theta e^{-u}du = -2u \theta e^{-u}|^{\infty}_0 + 2 \theta \int^{\infty}_0 e^{-u} du =-2 \theta e^{-u} |^{\infty}_0 = 2 \theta[/tex]

    When I add them up, I get theta, but the answer is supposed to be (3/2)theta. Where did I make the mistake?
  2. jcsd
  3. Jan 19, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Well, you just dropped a '2' factor. Maybe more than once. For example, why doesn't your boundary term in the first integration by parts have a '2' in it? I really don't want to check every term. But you should have gotten -theta/2 for the first integral.
  4. Jan 19, 2010 #3
    I did forget a 2 in the first integration by parts, but it equals to 0 so it wouldn't make much of a difference. But I did realise my mistake. I didnt diffrentiate the e^-2u properly in the second part.
  5. Jan 19, 2010 #4


    User Avatar
    Science Advisor
    Homework Helper

    That's true. Thanks for helping with the checking work!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Integration Parts separately Date
Integration by parts/substitution Nov 2, 2017
Solving an Integral Sep 23, 2017
Separable differential equation and Integration by parts Dec 14, 2010
Integration using separation of parts Apr 13, 2010