The value of (where

MATHEMATICS · Single correct · ISC · Mathematics · Physics · Calculus

Problem

The value of ∫110π([sec⁡−1x]+[cot⁡−1x])dx\int_{1}^{10\pi} ([\sec^{-1} x] + [\cot^{-1} x]) dx (where, [⋅][\cdot] denotes the greatest integer function) is equal to (1) (sec⁡1)−10π(\sec 1) - 10\pi (2) 10π−sec⁡110\pi - \sec 1 (3) π−sec⁡1\pi - \sec 1 (4) None of these

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