Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Double integrals that involve integration by parts

  1. Jul 2, 2010 #1
    1. The problem statement, all variables and given/known data

    Evaluate the double integral.

    2. Relevant equations

    integral by part: uv - integral of v*du

    3. The attempt at a solution

    I wrote out my works. And I am just stuck at the x integration....

    Please click on the links to see the pictures. I don't want to resize it which may reduce the quality.


    I tried to break the last integration into three parts, which each had x^2 at the bottom. But then the integration by parts seem impossible...

    The answer to the question is 19/2 - 1/2e^6
    I am sure the first part with respect to y is correct (I verified that with wolframalpha).

    Any help would be appreciate. Thank you

    * I believe doing dx first is easier, if I am correct. But I already started, so I just want to see how can i crack down with dy first. There can be ugly expression during exam too.
    Last edited: Jul 2, 2010
  2. jcsd
  3. Jul 2, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Doing it dx first is a LOT easier. If you do it dy first you need incomplete gamma functions to write down an indefinite integral (as you are discovering). There's no elementary way (like integration by parts) to do that integral.
  4. Jul 2, 2010 #3
    oh god. lol
    thanks Dick. I see what you mean :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook