# Integral to the Maximum

**Calculus**Level 4

\[ \int _{ 0 }^{ 2n\pi }{ \max \left( \sin x, { \sin }^{ -1 } (\sin x) \right)dx } = \ ? \]

Note that \(n\) is an integer.

\[ \int _{ 0 }^{ 2n\pi }{ \max \left( \sin x, { \sin }^{ -1 } (\sin x) \right)dx } = \ ? \]

Note that \(n\) is an integer.

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