Let's insert 1729 again and again

Calculus Level 5

Given : 02×1729πmax{sinx,sin1(sinx)} dx=a\int_{0}^{2 \times 1729\pi} \max\{\sin x, \sin^{-1}(\sin x)\} \ dx=a

Find the value of a\lceil a \rceil

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Note : ..\lceil .. \rceil denotes the Ceiling Function( lowest integer greater than equal to).

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