Determine the Dot's Distance

Calculus Level 3

The location of a dot \(P\) at a given time \(t\) in the \(xy\) plane is given by \((x,y) = (t - \sin t, 1 - \cos t)\). What is the distance traveled by \(P\) in the interval \(0 \leq t \leq 2\pi\)?

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