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Need some clarification Explain why 1 b 5 f (xrtly'rtJyrtix'itht measures the area of R provided that {x[t], y[t]} sweeps out the boundary of R

Need some clarification

Explain why 1 b 5 f (xrtly'rtJyrtix'itht measures the area of R provided that {x[t], y[t]} sweeps out the boundary of R exactly one time in the counterclockwise fashion as t advances from a to b. b

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