The area bounded by the curve \(\color{darkgreen}{f}(\color{blue}{x}) \) and its inverse function between the ordinates \(\color{blue}{x} = \color{darkblue}{0} \) and \(\color{blue}{x} = \color{darkblue}{2\pi}\), is

\[\large \color{darkgreen}{f}(\color{blue}{x}) = \color{blue}{x} + \color{purple}{sin}(\color{blue}{x}) \]

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