The value of

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

The value of ∫01⌊x+⌊x+⌊x⌋⌋⌋ dx\int_0^1\lfloor x+\lfloor x+\lfloor x\rfloor\rfloor\rfloor\,dx, where ⌊⋅⌋\lfloor\cdot\rfloor denotes the greatest integer function, is equal to (1) 22 (2) 33 (3) −3-3 (4) None of these

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