Solution Found!
Stokes' Theorem for evaluating surface integrals Evaluate
Chapter 13, Problem 17E(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.
\(\mathbf{F}=\langle x, y, z\rangle\); S is the upper half of the ellipsoid \(x^{2} / 4+y^{2} / 9+z^{2}=1\)
Text Transcription:
iint_S (nabla x F) cdot n dS
F = langle x, y, z rangle
x^2/4 = y^2/9 + z^2 = 1
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.
\(\mathbf{F}=\langle x, y, z\rangle\); S is the upper half of the ellipsoid \(x^{2} / 4+y^{2} / 9+z^{2}=1\)
Text Transcription:
iint_S (nabla x F) cdot n dS
F = langle x, y, z rangle
x^2/4 = y^2/9 + z^2 = 1
ANSWER:Solution 17EStep 1:Given thatF = x, y, z ; S is the upper half of the ellipsoid x2/4 + y2/9 + z2 = 1.