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Math Help - Surface Integrals

  1. #1
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    Surface Integrals

    Calculate the integral \int\int_{S} FdS, where is the surface of the half ball x^2 + y^2 +z^2 is less than or equal to1, z is greater than or equal to 0 and
    F = (x+3y^5,y+10xz,z-xy)
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  2. #2
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    As a matter of clarity, are you computing

    \displaystyle{\iint_{S}\vec{F}\cdot d\vec{S}=\iint_{S}\left(\vec{F}\cdot\hat{n}\right)  dS}?

    If so, what have you done so far?
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  3. #3
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    And, if so, is the surface to be oriented with upward or downward normals?
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  4. #4
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    Reply to HallsofIvy at Post # 3:

    Usually, in problems like this, the normal to the surface is oriented outward. That makes it unambiguous in most cases.
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