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Math Help - Double Integrals

  1. #1
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    Double Integrals

    Ok so i'm rather stuck on this one question, help would be much appreciated:


    I have used the capital S as an integral sign with the values above and below it as the limits of the integration, also please ignore the underscores, i put them in to aid with the spacing

    by changing the order of integration, evaluate

    y=4 x=y^0.5
    S_____S______exp(y/x) dx dy
    y=0 x=(y/2)

    Draw a sketch of the area and directions of integration.



    Thanks in advance
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, macabre!

    By changing the order of integration, evaluate:

    . . y=4 . .x=y^
    . .
    . . . . . e(y/x) dx dy
    . .y=0 . . x=y

    Draw a sketch of the area and directions of integration.
    Code:
            |
           4+         *
            |       *:|
            |     *::*|
            |   *:::* |
            | *:::*   |
          - * - - - - + -
            |         2

    . . x=2 . y=2x
    . .
    . . . . . e^{y/x} dy dx
    . . x=0 . y=x

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  3. #3
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    Joined
    Sep 2006
    Posts
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    Where do you then go from there?

    I have done the first integration (with respect to y)

    Which Gives

    2
    S exp(y/x){2x - x^2} dx
    0

    But i do not understand where to go from here; I have expanded to

    2
    S (2x)exp(y/x) - (x^2)exp(y/x) dx
    0

    but am lost as to how to then integrate this; am i meant to take the y value as a constant in order to give
    _______2
    exp(y) S (2x)exp(1/x) - (x^2)exp(1/x) dx
    _______0
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