Solution Found!
Answer: Stokes' Theorem for evaluating surface integrals
Chapter 13, Problem 19E(choose chapter or problem)
Stokes' Theorem for evaluating surface integrals Evaluate the line integral in Stokes' Theorem to evaluate the surface integral \(\iint_{S}(\nabla \times \mathbf{F}) \cdot \mathbf{n} d S\). Assume that n is in the positive z-direction.
\(\mathbf{F}=\langle 2 y,-z, x-y-z\rangle\); S is the cap of the sphere (excluding its base) \(x^{2}+y^{2}+z^{2}=25\), for \(3 \leq x \leq 5\)
Text Transcription:
iint_S (nabla x F) cdot n dS
F = langle 2y, -z, x - y - z rangle
x^2 + y^2 + z^2 = 25
3 leq x leq 5
Questions & Answers
QUESTION:
Stokes' Theorem for evaluating surface integrals Evaluate the line integral in Stokes' Theorem to evaluate the surface integral \(\iint_{S}(\nabla \times \mathbf{F}) \cdot \mathbf{n} d S\). Assume that n is in the positive z-direction.
\(\mathbf{F}=\langle 2 y,-z, x-y-z\rangle\); S is the cap of the sphere (excluding its base) \(x^{2}+y^{2}+z^{2}=25\), for \(3 \leq x \leq 5\)
Text Transcription:
iint_S (nabla x F) cdot n dS
F = langle 2y, -z, x - y - z rangle
x^2 + y^2 + z^2 = 25
3 leq x leq 5
ANSWER:Problem 19E (F)n = -32The val