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Thread: Triple Intergral

  1. #1
    Member Ranger SVO's Avatar
    Apr 2006
    Abilene Tx

    Triple Intergral

    #14 f(x,y,z) = z W is the region in the first octant bounded by the cylinder y^2 + z^2 = 9 and the planes y = x, x = 0 and z = 0

    My first intergral has the limits between x = 0 and x = y^2 + z^2 - 9

    My second intergral has limits between z = 0 and z = sqrt(9-y^2)

    My final intergral ranges in between y = 0 and y = 3

    I dont think it right because I end up with a negative answer

    I end up with -162/5

    What am I doing wrong????????????????????????
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  2. #2
    Global Moderator

    Nov 2005
    New York City
    Sorry I do not have a 3-d grapher, so accept my hand drawing, on the bottom.

    So we are finding,
    $\displaystyle \int \int_V \int z \, dV$
    Which by Fubini's theorem is,
    $\displaystyle \int_A \int \int_0^{\sqrt{9-y^2}} z \, dz\, dA$
    Where $\displaystyle A$ is your region.
    Which is,
    $\displaystyle \int_0^3 \int_x^3 \int_0^{\sqrt{9-y^2}} z\, dz\, dy\, dx$
    Attached Thumbnails Attached Thumbnails Triple Intergral-picture4.gif  
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