# Optimization and integration

Calculus Level 3

Let $$K$$ be the rectangle inscribed in the region bounded by the curve $$y = \cos x$$ and the lines $$x = - \pi/2, x =\pi/2$$ and $$y=0$$ with the largest possible area. Let $$R$$ be the region below the curve defined by $$y = \cos x$$ but above the $$x$$ axis. If $$A$$ denotes the area of the region not in the rectangle $$K$$ but in the region $$R$$, find $$\lfloor 1000A \rfloor$$.

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