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Math Help - question on outward flux (Vector calc.)

  1. #1
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    question on outward flux (Vector calc.)

    Hi,

    I need help with this question;

    Find the outward flux of the vector field F = <y,x,-z> through the boundary of the solid inside the cylinder (x^2) + (y^2) = 4 between the plane z = 0 and the paraboloid z = (x^2) + (y^2)
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Ideally you know the divergence thm --an ideal place yo use it

    the flux in this case is equal to the volume since div(F) = 1

    If not you have some work to do

    You'll need 4 flux integrals

    1. on the bottom but here z = 0 so the flux is 0

    the parabaloid intersects the cylinder in the plane z =4

    2. through the sides of the cylinder below z = 4 (split into right and left halves)

    3. through the parabaloid above over the circle r = 2
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