Solution Found!
Line integrals of vector fields on closed curves Evaluate
Chapter 13, Problem 33E(choose chapter or problem)
Evaluate \(\oint_{C} \mathbf{F} \cdot d \mathbf{r}\) for the following vector fields and closed oriented curves C by parameterizing C. If the integral is not zero, give an explanation.
\(\mathbf{F}=\langle x, y\rangle\); C is the circle of radius 4 centered at the origin oriented counterclockwise.
Questions & Answers
QUESTION:
Evaluate \(\oint_{C} \mathbf{F} \cdot d \mathbf{r}\) for the following vector fields and closed oriented curves C by parameterizing C. If the integral is not zero, give an explanation.
\(\mathbf{F}=\langle x, y\rangle\); C is the circle of radius 4 centered at the origin oriented counterclockwise.
ANSWER:Solution 33E
Step 1:
Given that
F = 〈x, y〉; C is the circle of radius 4 centered at the origin oriented counterclockwise.