Verify Stokes' theorem for the given surface S and boundary S, and vector fields F. S = {(x, y, z): z = 1 - x² - y², z ≥ 0}, (oriented as a graph) as = {(x, y) : x² + y² = 1} JS F = las zi + xj + (6zx + 4xy)k (V x F) · ds = F. ds =

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Verify Stokes' theorem for the given surface S and boundary S, and vector fields F.
(oriented as a graph)
S = {(x, y, z): z = 1 - x² - y², z ≥ 0},
{(x, y) x² + y² = 1}
as
:
F = zi + xj + (6zx + 4xy)k
1/₂ (VxF).
IS
=
(V x F) ds =
F. ds =
Jas
Transcribed Image Text:Verify Stokes' theorem for the given surface S and boundary S, and vector fields F. (oriented as a graph) S = {(x, y, z): z = 1 - x² - y², z ≥ 0}, {(x, y) x² + y² = 1} as : F = zi + xj + (6zx + 4xy)k 1/₂ (VxF). IS = (V x F) ds = F. ds = Jas
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