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Evaluating line integrals Evaluate the line
Chapter 13, Problem 25RE(choose chapter or problem)
Evaluating line integrals Evaluate the line integral \(\int_{C} \mathbf{F} \cdot d \mathbf{r}\) for the following vector fields F and curves C in two ways.
a. By parameterizing C
b. By using the Fundamental Theorem for line integrals, impossible
\(\mathbf{F}=\nabla(x y z) ; C: \mathbf{r}(\mathrm{t})=\langle\cos t, \sin t, t / \pi\rangle\), for \(0 \leq t \leq \pi\)
Text Transcription:
int_C F cdot dr
F = nabla(xyz); C: r(t) = langle cos t, sin t, t/pi rangle
0 leq t leq pi
Questions & Answers
QUESTION:
Evaluating line integrals Evaluate the line integral \(\int_{C} \mathbf{F} \cdot d \mathbf{r}\) for the following vector fields F and curves C in two ways.
a. By parameterizing C
b. By using the Fundamental Theorem for line integrals, impossible
\(\mathbf{F}=\nabla(x y z) ; C: \mathbf{r}(\mathrm{t})=\langle\cos t, \sin t, t / \pi\rangle\), for \(0 \leq t \leq \pi\)
Text Transcription:
int_C F cdot dr
F = nabla(xyz); C: r(t) = langle cos t, sin t, t/pi rangle
0 leq t leq pi
ANSWER:Solution 25REStep 1