Solution Found!
Verifying Stokes' Theorem Verify that the line integral
Chapter 13, Problem 5E(choose chapter or problem)
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.
\(\mathbf{F}=\langle y,-x, 10\rangle\); S is the upper half of the sphere \(x^{2}+y^{2}+z^{2}=1\) and C is the circle \(x^{2}+y^{2}=1\) in the xy-plane.
Questions & Answers
QUESTION:
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.
\(\mathbf{F}=\langle y,-x, 10\rangle\); S is the upper half of the sphere \(x^{2}+y^{2}+z^{2}=1\) and C is the circle \(x^{2}+y^{2}=1\) in the xy-plane.
ANSWER:Solution 5E