Question
Use Stokes' Theorem to evaluate
S
curl F · dS.
F(x, y, z) = 2y cos z i + ex sin z j + xey k,
S is the hemisphere x2 + y2 + z2 = 49, z ≥ 0, oriented upward.
S
curl F · dS.
F(x, y, z) = 2y cos z i + ex sin z j + xey k,
S is the hemisphere x2 + y2 + z2 = 49, z ≥ 0, oriented upward.
Answers
The curve for the line integral is just
x = 9cos(t)
y = 9sin(t)
z = 0
Now just evaluate F.dr and integrate for t in [0,2pi]
x = 9cos(t)
y = 9sin(t)
z = 0
Now just evaluate F.dr and integrate for t in [0,2pi]
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