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
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