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Double integrals, trying to be sure I am not doing something wrong

  1. May 12, 2013 #1
    1. evaluate the following:

    [itex]\int^{1}_{0}[/itex][itex]\int[/itex][itex]^{1}_{0}[/itex]xyex+y dydx


    3. The attempt at a solution

    OK, so this should be pretty simple. But for some reason I am having trouble integrating the yex+y bit with respect to y. If I do it by parts I end up with iterations like this:

    [itex]\int^{1}_{0}[/itex]xyex+y - [itex]\int^{}_{}[/itex]ex+yxdy dx

    And integrating again I got

    [itex]\int^{1}_{0}[/itex]xyex+y - ex+yx [itex]|^{1}_{0}[/itex] dx


    plugging in the relevant values I got

    [itex]\int^{1}_{0}[/itex]xex+1-xex+1 - xex + xexdx

    which with the latter terms cancelling gets you


    [itex]\int^{1}_{0}[/itex]xex+1-xex+1 dx


    And the whole thing should go to zero.

    OK, did I do this whole bit correctly? I want to make sure that I am not doing something stupid. If I did it right, wonderful. (I know this might sound kind of silly to post a problem that I think I did correctly, but it never hurts to have another pair of eyes)
     
  2. jcsd
  3. May 12, 2013 #2

    LCKurtz

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    I don't have time to run through your work right now, but surely something is wrong since your integrand is positive. You must have a positive result. Why don't you try writing ##e^{x+y} = e^xe^y## and separate the integrals. Really easy then.
     
  4. May 12, 2013 #3
    You're correct up to here. After here is where your solution diverges from correct solution.

    P.S. It may be helpful in the future to check computationally:
     
  5. May 12, 2013 #4
    Thanks, I did it again and I realized I forgot the y component. D'OH!
     
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