the z-axis and above the x-y plane. Use Stokes' Theorem to calculate the circulation of F = (x + y?, 2x3 – yz, -y² + 3x²y+ z) around the boundary of S (a half-ellipse) in the counter-clockwise direction when viewed from above.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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Let S be the portion of the plane z = 2x that is inside the cylinder of radius R centered around
the z-axis and above the x-y plane. Use Stokes' Theorem to calculate the circulation of
– yz, -y² + 3x²y+ z)
,2,
F
(x + y², 2x³
around the boundary of S (a half-ellipse) in the counter-clockwise direction when viewed from
above.
Transcribed Image Text:Let S be the portion of the plane z = 2x that is inside the cylinder of radius R centered around the z-axis and above the x-y plane. Use Stokes' Theorem to calculate the circulation of – yz, -y² + 3x²y+ z) ,2, F (x + y², 2x³ around the boundary of S (a half-ellipse) in the counter-clockwise direction when viewed from above.
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