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Changing the order of a triple integration

  1. Apr 5, 2010 #1
    I'm given this definite integral:
    [itex]\int_0^{1}\int_{\sqrt{x}}^{1}\int_{0}^{1-y}f(x,y,z)dzdydx[/itex]

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

    24on636.png

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

    How do I find the limits of y?
     
  2. jcsd
  3. Apr 5, 2010 #2

    Mark44

    Staff: Mentor

    Just look at the original iterated integral to see the region over integration occurs.

    z = 0 to z = 1 - y
    y = sqrt(x) to y = 1
    x = 0 to x = 1.

    Sketch that region and it will help you determine the limits of integration for a different order of integration.
     
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