Sliding Sine Window

Calculus Level 5

A square of side length one rests in the first quadrant with two of its sides sitting on the coordinate axes, overlapping the region between \(y = \sin x\) and the \(x\)-axis. It then slides along the positive \(x\)-axis at a rate of 1 unit per second as shown above.

At what rate is the area inside both the blue region and the square changing after 1 second?

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