If for a real number

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

If for a real number yy, [y][y] is the greatest integer less than or equal to yy, then find the value of the integral ∫π/23π/2[2sin⁡x]dx\int_{\pi/2}^{3\pi/2} [2 \sin x] dx.

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