Use Stokes' Theorem to evaluate: where 11 curl F ndS F(x, y, z) = xi+yj+xyzk and S is the part of the sphere x² + y² + z² = 4, z ≥ 0 that lies above th xy-plane oriented upward. Hint: Do NOT compute the curl, do NOT compute the surface integral, use Stokes and find the boundary curve C.

Use Stokes' Theorem to evaluate: where 11 curl F ndS F(x, y, z) = xi+yj+xyzk and S is the part of the sphere x² + y² + z² = 4, z ≥ 0 that lies above th xy-plane oriented upward. Hint: Do NOT compute the curl, do NOT compute the surface integral, use Stokes and find the boundary curve C.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.4: Polyhedrons And Spheres

Problem 48E: Sketch the solid that results when the given circle of radius length 1 unit is revolved about the...

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Question

27) Use Stokes' Theorem to evaluate:
1150
where
curlF ndS
F(x, y, z) = xi+yj + xyzk
and S is the part of the sphere x² + y² + z² = 4, z ≥ 0 that lies above th
xy-plane oriented upward.
Hint: Do NOT compute the curl, do NOT compute the surface integral,
use Stokes and find the boundary curve C.

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