Question

Evaluate the surface integral 

 
 
S
F · dS

 for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x, y, z) = yi − xj + 2zk, S is the hemisphere 

x2 + y2 + z2 = 4,  z ≥ 0, oriented downward
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