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

Chapter 15, Problem 49

(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.

\(\mathbf{F}(x, y)=\left(x^{3}-2 x^{2}\right) \mathbf{i}+\left(x-\frac{y}{2}\right) \mathbf{j}\)

\(C: \mathbf{r}(t)=t \mathbf{i}+t^{2} \mathbf{j}\)

Text Transcription:

int_{C} F cdot dr = 0

F(x, y) = (x^3 -2x^2)i + (x - y / 2) j

C: r(t) = ti + t^{2}j

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