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Find the work done by the force field $$ \textbf{F}(x, y) = x \, \textbf{i} + (y + 2) \, \textbf{j} $$ in moving an object along an arch of the cycloid

$ \textbf{r}(t) = (t - \sin t) \, \textbf{i} + (1 - \cos t) \, \textbf{j} $ $ 0 \leqslant t \leqslant 2\pi $

Work done $=2 \pi^{2}$

Vector Calculus

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