Answer: Evaluating a Line Integral of a Vector Field In Exercises 1124, find the value
Chapter 15, Problem 13(choose chapter or problem)
In Exercises 11 - 24, find the value of the line integral
\(\int_{C} \mathbf{F} \cdot d \mathbf{r}\).
(Hint: If F is conservative, the integration may be easier on an alternative path.)
\(\mathbf{F}(x, y)=y \mathbf{i}-x \mathbf{j}\)
(a) \(\mathbf{r}_{1}(t)=t \mathbf{i}+t \mathbf{j}, \quad 0 \leq t \leq 1\)
(b) \(\mathbf{r}_{2}(t)=t \mathbf{i}+t^{2} \mathbf{j}, \quad 0 \leq t \leq 1\)
(c) \(\mathbf{r}_{3}(t)=t \mathbf{i}+t^{3} \mathbf{j}, \quad 0 \leq t \leq 1\)
Text Transcription:
int_C F cdot dr
F(x, y) = yi - xj
r_1 (t) = ti + tj, 0 leq t leq 1
r_2 (t) = ti + t^{2}j, 0 leq t leq 1
r_3 (t) = ti + t^{3}j, 0 leq t leq 1
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