1. ## Surface Integrals

Calculate the integral $\int\int_{S} F$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
$F = (x+3y^5,y+10xz,z-xy)$

2. 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?

3. And, if so, is the surface to be oriented with upward or downward normals?

4. 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.