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Evaluating line integrals Evaluate the line
Chapter 13, Problem 24RE(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
\(\mathbf{F}=\nabla\left(x^{2} y\right) ; C: \mathbf{r}(t)=\left\langle 9-t^{2}, t\right\rangle\), for \(0 \leq t \leq 3\)
Text Transcription:
int_C F cdot dr
F = nabla(x^2y); C: r(t) = langle 9 - t^2, t rangle
0 leq t leq 3
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
\(\mathbf{F}=\nabla\left(x^{2} y\right) ; C: \mathbf{r}(t)=\left\langle 9-t^{2}, t\right\rangle\), for \(0 \leq t \leq 3\)
Text Transcription:
int_C F cdot dr
F = nabla(x^2y); C: r(t) = langle 9 - t^2, t rangle
0 leq t leq 3
ANSWER:Solution 24RE
Step 1
