The value of

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The value of ∫−π/2π/2[cot⁡−1x] dx\int_{-\pi/2}^{\pi/2}[\cot^{-1}x]\,dx, where [⋅][\cdot] denotes the greatest integer function, is (1) π+cot⁡1\pi+\cot1 (2) π+cot⁡2\pi+\cot2 (3) π+cot⁡1+cot⁡2\pi+\cot1+\cot2 (4) cot⁡1+cot⁡2\cot1+\cot2

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