Solution Found!
Solved: Stokes' Theorem for evaluating line integrals
Chapter 13, Problem 15E(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.
\(\mathbf{F}=\left\langle y^{2},-z^{2}, x\right\rangle\); C is the circle \(\mathbf{r}(t)=\langle 3 \cos t, 4 \cos t, 5 \sin t\rangle\)
Text Transcription:
Oint_c F cdot dr
F = langle y^2, -z^2, x rangle
r(t) = langle 3 cos t, 4 cos t, 5 sin t rangle
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.
\(\mathbf{F}=\left\langle y^{2},-z^{2}, x\right\rangle\); C is the circle \(\mathbf{r}(t)=\langle 3 \cos t, 4 \cos t, 5 \sin t\rangle\)
Text Transcription:
Oint_c F cdot dr
F = langle y^2, -z^2, x rangle
r(t) = langle 3 cos t, 4 cos t, 5 sin t rangle
ANSWER:Solution 15EStep 1:Given thatF = y2, -z2, x ; C is the circle r(t) = 3 cos t, 4 cos t, 5 sin t, for 0 f 2.