Let's insert 1729 again and again

Calculus Level 4

Given : \[\int_{0}^{2 \times 1729\pi} \max\{\sin x, \sin^{-1}(\sin x)\} \ dx=a\]

Find the value of \(\lceil a \rceil\)

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

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