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Thread: Graphing region of integration of triple integral ∫01∫01-x^2∫01-x f(x,y,z)dzdydx

  1. #1

    Graphing region of integration of triple integral ∫01∫01-x^2∫01-x f(x,y,z)dzdydx

    We have to consider the integral of
    0101-x^201-x f(x,y,z)dzdydx


    First we're told to graph the region of integration, so I started that but I'm not exactly sure what I'm doing. I end up with something that looks like a slim triangular slice of a cone, but I don't know if it's correct. Is it? Please help

    We also have to write the integral in 5 other ways and I'm not sure how.

  2. #2
    Elite Member
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    I can't help you with the drawing, but you have...

    z = 1 - x -- That's a nice lean-to.
    y = 1 - x^2 -- That's a nice parabolic cap.

    You have everything starting at 0, so we're in the first octant.

    Your integral is dzdydx, the five other ways are:

    dzdxdy
    dydzdx
    dydxdz
    dxdydz
    dxdzdy

    Your only stopping point should be x = f(y). Make sure you pick the positive branch.
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

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