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Solved: Verifying Stokes' Theorem Verify that the line
Chapter 13, Problem 6E(choose chapter or problem)
Verifying Stokes’ Theorem Verify that the line integral and the surface integral of Stokes' Theorem are equal for the following vector fields, surfaces S, and closed curves C. Assume that C has counterclockwise orientation and S has a consistent orientation.
\(\mathbf{F}=\langle 0,-x, y\rangle\); S is the upper half of the sphere \(x^{2}+y^{2}+z^{2}=4\) and C is the circle \(x^{2}+y^{2}=4\) in the xy-plane.
Text Transcription:
F = langle 0,-x, y rangle
x^2 + y^2 + z^2 = 4
x^2 + y^2 = 4
Questions & Answers
QUESTION:
Verifying Stokes’ Theorem Verify that the line integral and the surface integral of Stokes' Theorem are equal for the following vector fields, surfaces S, and closed curves C. Assume that C has counterclockwise orientation and S has a consistent orientation.
\(\mathbf{F}=\langle 0,-x, y\rangle\); S is the upper half of the sphere \(x^{2}+y^{2}+z^{2}=4\) and C is the circle \(x^{2}+y^{2}=4\) in the xy-plane.
Text Transcription:
F = langle 0,-x, y rangle
x^2 + y^2 + z^2 = 4
x^2 + y^2 = 4
ANSWER:Solution 6E
The circulation integral is F
r = -4
The integral of cos