The value of the definite integral equals

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

The value of the definite integral ∫02πnmax⁡(sin⁡x,sin⁡−1(sin⁡x)) dx\int_0^{2\pi n}\max\left(\sin x,\sin^{-1}(\sin x)\right)\,dx equals, where nn is a positive integer: (1) n(π2−4)2\dfrac{n(\pi^2-4)}{2} (2) n(π2−4)4\dfrac{n(\pi^2-4)}{4} (3) n(π2−8)4\dfrac{n(\pi^2-8)}{4} (4) n(π2−2)4\dfrac{n(\pi^2-2)}{4}

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