Functions and Integrals 1

Calculus Level 4

Let \(f: \mathbb R \to \mathbb R\) be defined as \(f(x) = \sin x + x\). If \(\displaystyle \int_0^\pi f^{-1} (x) \, dx = \dfrac{\pi^2}2 - k\), find the value of \(k\).

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