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Calculate the upward flux

  1. Dec 9, 2008 #1
    1. The problem statement, all variables and given/known data
    Let S be part of the plane 3x + 2y + z =9 lying in the first octant. Calculate the upward flux of vectorF(x,y,z) = x i + xy j + xz k

    2. Relevant equations

    F(dot)(-dz/dx i - dz/dy j + k)

    3. The attempt at a solution

    x i + xy j + xz k (dot) (3i +2j + k)=3x + 2xy + xz
    I then substituted z: =3x + 2xy + 9x -3x^2 - 2xy

    [tex]\int[/tex][tex]\int[/tex] -3x^2 + 12x dydx

    0 [tex]\leq[/tex] y [tex]\leq[/tex] -4.5x/3 + 4.5
    0 [tex]\leq[/tex] x [tex]\leq[/tex] 3

    Any help on whether this is correct or not would be apprecitated
  2. jcsd
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