Minimizing Integral

Calculus Level 4

\[ \large \int_0^\pi | \sin x - Ax | \, dx \]

Find the value of \(A\) such that the value of the integral above is minimized. If the value of \(A\) can be expressed as \[ \dfrac{\sqrt P}{\pi^Q} \sin \left ( \dfrac{\pi}{\sqrt R} \right) , \] submit your answer as \(P+Q+R\).

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