Stokes' Theorem for evaluating surface integrals Evaluate

Chapter 13, Problem 17E

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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

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.

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