Track & Trace

Calculus Level 3

The ends of a stiff bar AB\overline{AB} of length 4 slide freely inside a parabolic track (specifically, the parabola y=x2y=x^2). As they do, the midpoint MM of that bar traces a curve. Find the area of the region between the parabola and the curve traced by MM.

Assume that the bar slides infinitely in both directions.

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