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Double integration problem

  1. Mar 28, 2009 #1
    1. The problem statement, all variables and given/known data

    \int^1_y\int^1_0 x^2*e^{xy} dydx

    Answer: [tex]1/2 (e-2)[/tex]

    3. The attempt at a solution

    I've tried about 4 ways of doing this, I can't solve it. It either ends up being a completely huge and wrong answer, or ends up giving me a integration by parts of something like [tex]\int e^(x^2) dx[/tex] which I cant solve
    Last edited: Mar 28, 2009
  2. jcsd
  3. Mar 29, 2009 #2


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    Homework Helper

    Hi Enzo! :smile:

    (have an integral: ∫ and try using the X2 tag just above the Reply box :wink:)
    Did you change the order of integration first?

    I get ∫xex2 dx, which is easy :wink:

    Try again! :smile:
  4. Mar 29, 2009 #3


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    This makes no sense. The way you have it written, with the "outer integral" from y to 1, the answer must be a function of y, not a constant. But, as written it does not give "[itex]e^{x^2}[/itex]
    [tex]\int_{x=y}^1\int_{y= 0}^1 x^2e^{xy}dy dx= \int_{x=y}^1\left(xe^{xy}\right)_0^1 dx[/tex]
    [tex]= \int_{x=y}^1 \left(xe^x- x\right)dx[/tex]
    which can be done by a single integration by parts.

    If it were
    [tex]\int_{y=0}^1\int{x=y}^1 x^2e^{xy}dx dy[/itex]
    tat can be done by two integrations by parts.
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