Solved: Evaluate. with F and C as given, by the method that seems most suitable. Recall

Chapter 10, Problem 10.1.209

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Evaluate, with \(\mathbf{F}\) and C as given, by the method that seems most suitable. Recall that if \(\mathbf{F}\) is a force, the integral gives the work done in a displacement along C. (Show the details.)

\(\mathbf{F}=\left[x^{2}, y^{2}, y^{2} x\right]\),

C the helix \(\mathbf{r}=\left[\begin{array}{lll}2 \cos t . & 2 \sin t, & 6 t\end{array}\right]\) from (2.0.0) to \((0.2,3 \pi)\)

Text Transcription:

F

\(\mathbf{F}=\left[x^{2}, y^{2}, y^{2} x\right]\),

r = [2 cos t .  2 sin t,  6t]

(0.2,3 pi)

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