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Math Help - Surface Integrals of Flux

  1. #1
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    Surface Integrals of Flux

    Hi, am kinda having trouble figuring out the following problem? any help would be highly appreciated...


    Evaluate if and the surface S is given by for . (Take S to have upward orientation.)


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  2. #2
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    Quote Originally Posted by althaemenes View Post
    Hi, am kinda having trouble figuring out the following problem? any help would be highly appreciated...


    Evaluate if and the surface S is given by for . (Take S to have upward orientation.)


    if \vec F(x,y,z)=P \vec i +Q \vec j + R \vec k and z=g(x,y) then

    \iint_S \vec F \cdot d\vec S=\iint_D\left( -P \frac{\partial z}{\partial x}-Q \frac{\partial z}{\partial y}+R\right)dA

    This gives us

    \int \int (2xy\sin(8y)+4xy^2(8x\cos(8y))-2y(x\sin(8y)))dA
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  3. #3
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    help

    Quote Originally Posted by TheEmptySet View Post
    if \vec F(x,y,z)=P \vec i +Q \vec j + R \vec k and z=g(x,y) then

    \iint_S \vec F \cdot d\vec S=\iint_D\left( -P \frac{\partial z}{\partial x}-Q \frac{\partial z}{\partial y}+R\right)dA

    This gives us

    \int \int (2xy\sin(8y)+4xy^2(8x\cos(8y))-2y(x\sin(8y)))dA

    okay, so I integrate

    \int \int (2xy\sin(8y)+4xy^2(8x\cos(8y))-2y(x\sin(8y)))dA[/quote]

    with x = 0 to pi/16 and y = 0 to pi/16

    and keep getting:

    7.37119946071407E-05

    I was wondering if I am using the right limits:

    Please help..
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