Inverse Area with definite integration.!

Calculus Level 4

If \(f: \mathbb {R \to R}\), \(f(x)=x+\sin x\), then find the value of

\[\large \int_{0}^{\pi} f^{-1}(x) \ dx\]

Note : \(f^{-1}(x)\) denotes the inverse function of \(f(x)\).

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