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Triple Integral Domain

  1. Nov 14, 2011 #1
    1. The problem statement, all variables and given known data
    f(x,y,z,) = [itex]e^{2x-z}[/itex]
    W: x + y + z ≤ 1
    x, y, z ≥ 0

    2. Relevant equations

    3. The attempt at a solution
    For each domain, could you check it please?
    This is the only triple integral that's haunting me

    0 ≤ x ≤ 1-y-z
    0 ≤ y ≤ 1-x-z
    0 ≤ z ≤ 1-z-y
  2. jcsd
  3. Nov 14, 2011 #2


    Staff: Mentor

    I don't think you're on the right track here, at all. If you haven't already done so, sketch the region over which integration is to be done. The region is a tetrahedron that is bounded by the three coordinate planes and the plane x + y + z = 1. Where this plane intersects the x-y plane will play a role in your description of the region.
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