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Changing the order of integration for a triple integral?

  1. Nov 27, 2011 #1
    1. The problem statement, all variables and given/known data

    [itex]\int^{1}_{0}[/itex][itex]\int^{x}_{0}[/itex][itex]\int^{y}_{0}[/itex] f(x,y,z)dzdydx

    I need to write it in terms of dxdydz

    2. Relevant equations

    3. The attempt at a solution

    I've tried to draw the 3D representation. I don't really know how to change the order, I don't recall my teacher even showing us this. :confused: I know how to change the order of integration for double integrals, but not this. Any help would be appreciated.
  2. jcsd
  3. Nov 28, 2011 #2


    Staff: Mentor

    Have you started by sketching the region of integration (not the integrand). The region as described in your first iterated integral is:
    0 <= z <= y
    0 <= y <= x
    0 <= x <= 1
    Each of these inequalities describes two boundary planes. If you rewrite your integral with a different order of integration, you'll need to come up with a different description for the same region.
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