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Math Help - calculating flux through a surface

  1. #1
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    calculating flux through a surface

    My question is:

    Compute the flux of the vector field, \vec{F} , through the surface, S.
    \vec{F} = 7\vec{r} and S is the part of the surface z = x^2 + y^2 above the disk x^2 + y^2 \leq 4 oriented downward.

    My answer so far is

    \int\limits_R (7x\vec{i} + 7y\vec{j} + (x^2 + y^2)\vec{k}) \cdot (2x\vec{i} + 2y\vec{j} - k) dA
    \int\limits_R (14x^2 + 14y^2 - (x^2 + y^2)) dA
    \int\limits_R (13x^2 + 13y^2) dA
    13 \int\limits_R (x^2 + y^2) dA
    13 \int^{2\pi}_0\int^2_0 r^3 dr d\theta
    13 \int^{2\pi}_0 4 d\theta

    104\pi

    is this correct?
    Last edited by TheRekz; April 21st 2009 at 03:40 PM.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    yes but for one cosmetic change

    in you next to last integral you should have replaced dA with drdtheta since dA is rdrdtheta


    --in your last integral dA should be dtheta
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  3. #3
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    ok my bad , edited my original post, however my final result that I got is:

    1664\pi, and this is a web assign question and it doesn't accepts it (marks it as wrong)
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  4. #4
    MHF Contributor Calculus26's Avatar
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    Aah-- I didn't see it either r varies from 0 to 2 not 4

    The radius of the disk is 2
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  5. #5
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    I tried  104\pi and it doesn't work as well
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  6. #6
    MHF Contributor Calculus26's Avatar
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    In your first integral you have 7x +7y +z --should be 7x+7y+7z
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  7. #7
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    thanks I got it now
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