Calculate the integral $\displaystyle \int\int_{S} F$dS, 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

$\displaystyle F = (x+3y^5,y+10xz,z-xy)$

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- Aug 4th 2010, 01:50 PMlarryboi7Surface Integrals
Calculate the integral $\displaystyle \int\int_{S} F$d

**S**, 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

$\displaystyle F = (x+3y^5,y+10xz,z-xy)$ - Aug 4th 2010, 05:48 PMAckbeet
As a matter of clarity, are you computing

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

If so, what have you done so far? - Aug 5th 2010, 03:35 AMHallsofIvy
And, if so, is the surface to be oriented with upward or downward normals?

- Aug 5th 2010, 04:41 AMAckbeet
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.