Solution: Demonstrate a Property In Exercises 4750, demonstrate the property that

Chapter 15, Problem 50

(choose chapter or problem)

In Exercises 47 - 50, demonstrate the property that

\(\int_{C} \mathbf{F} \cdot d \mathbf{r}=0\)

regardless of the initial and terminal points of C, where the tangent vector r ‘(t) is orthogonal to the force field F.

\(\mathbf{F}(x, y)=x \mathbf{i}+y \mathbf{j}\)

\(C: \mathbf{r}(t)=3 \sin t \mathbf{i}+3 \cos t \mathbf{j}\)

Text Transcription:

int_{C} F cdot dr = 0

F(x, y) = xi + yj

C: r(t) = 3 sin ti + 3 cos tj