Question

Evaluate the surface integral S F · dS for the given vector field F and the...

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

Math   Calculus   
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