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Solution: Stokes' Theorem for evaluating surface integrals
Chapter 13, Problem 20E(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.
\(\mathbf{F}=\langle x+y, y+z, z+x\rangle\); S is the tilted disk enclosed by \(\mathbf{r}(t)=\langle\cos t, 2 \sin t, \sqrt{3} \cos t\rangle\)
Text Transcription:
iint_S (nabla x F) cdot n dS
F = langle x + y, y + z, z+ x rangle
r(t) = langle cost t, 2 sin t, sqrt3 cos t rangle
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.
\(\mathbf{F}=\langle x+y, y+z, z+x\rangle\); S is the tilted disk enclosed by \(\mathbf{r}(t)=\langle\cos t, 2 \sin t, \sqrt{3} \cos t\rangle\)
Text Transcription:
iint_S (nabla x F) cdot n dS
F = langle x + y, y + z, z+ x rangle
r(t) = langle cost t, 2 sin t, sqrt3 cos t rangle
ANSWER:
Solution 20E