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Problem 32 Hard Difficulty

(a) Find the work done by the force field $ \textbf{F} (x, y) = x^2 \, \textbf{i} + xy \, \textbf{j} $ on a particle that moves once around the circle $ x^2 + y^2 = 4 $ oriented in the counter-clockwise direction.
(b) Use a computer algebra system to graph the force field and circle on the same screen. Use the graph to explain your answer to part (a).

Answer

a) Work done is 0
b) $$
\int_{C} F \cdot d r=0
$$

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Video Transcript

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