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Solution: Stokes' Theorem for evaluating line integrals
Chapter 13, Problem 12E(choose chapter or problem)
Stokes' Theorem for evaluating line integrals Evaluate the line integral ac \(\oint_{C} \mathbf{F} \cdot d \mathbf{r}\) by evaluating the surface integral in Stokes ' Theorem with an appropriate choice of S. Assume that C has a counterclockwise orientation.
\(\mathbf{F}=\langle y, x z,-y\rangle\); C is the ellipse \(\(x^{2}+y^{2} / 4=1\) in the plane z = 1.
Text Transcription:
Oint_c F cdot dr
F = langle y, xz, -y rangle
x^2 + y^2/r = 1
Questions & Answers
QUESTION:
Stokes' Theorem for evaluating line integrals Evaluate the line integral ac \(\oint_{C} \mathbf{F} \cdot d \mathbf{r}\) by evaluating the surface integral in Stokes ' Theorem with an appropriate choice of S. Assume that C has a counterclockwise orientation.
\(\mathbf{F}=\langle y, x z,-y\rangle\); C is the ellipse \(\(x^{2}+y^{2} / 4=1\) in the plane z = 1.
Text Transcription:
Oint_c F cdot dr
F = langle y, xz, -y rangle
x^2 + y^2/r = 1
ANSWER:Solution 12E
The surface integral in Stokes’ Theorem is