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Homework Help: Flux of a Paraboloid without Parametrization

  1. Nov 30, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the outward flux of F = <x + z, y + z, xy> through the surface of the paraboloid z = x^2 + y^2, 0 ≤ z ≤ 4, including its top disk.

    2. Relevant equations

    double integral (-P(∂f/∂x) - Q(∂f/∂y) + R)dA
    where the vector F(x,y) = <P, Q, R>
    and where z = f(x,y) <-- f(x,y) is the function that undergoes partial differentiaion

    3. The attempt at a solution

    I didn't parametrize. My teacher wanted this method, where sum the surface integrals of two instances: a) when z = x^2 + y^2, and b) z = 4. My final answer was -32pi/3, with the flux at z = 4 being 0. I have a strong feeling I did something wrong but I don't know what. Please help. Any input will be greatly appreciated.
  2. jcsd
  3. Nov 30, 2011 #2


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    Science Advisor
    Homework Helper
    Gold Member

    Why would you say the flux is 0 when z = 4? But in any case, if you have something wrong how are we supposed to help you when you didn't show us your work?
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