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Math Help - Change order of a triple integration

  1. #1
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    Change order of a triple integration

    I'm given this definite integral:
    \int_0^{1}\int_{\sqrt{x}}^{1}\int_{0}^{1-y}f(x,y,z)dzdydx

    I need to change the order to dydxdz, but I'm stuck trying to get the limits of integration wrt y.



    \int_0^{1}\int_{x^2}^{0}\int_{}^{}f(x,y,z)dydzdx

    How do I find the limits of y?
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  2. #2
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    According to the integral, your region of integration is bounded by:

    1. the plane z=0
    2. the plane z=1-y
    3. the surface y=sqrt(x), and
    4. the plane x=0

    (that means your diagram is wrong, though)

    So I think the limits would be:
    y from sqrt(x) to 1-z
    z from 0 to 1-sqrt(x)
    x from 0 to 1

    - Hollywood
    Last edited by hollywood; April 6th 2010 at 08:30 AM. Reason: changed z limits
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