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Compute the average value of the function on the interval

Compute the average value of

    \[ f(x) = \cos x, \qquad -\frac{\pi}{2} \leq x \leq \frac{\pi}{2}. \]


We compute the average A(f),

    \[ A(f) = \frac{1}{\pi} \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos x \, dx = \frac{1}{\pi}\left(\sin \frac{\pi}{2} - \sin \frac{-\pi}{2} \right) = \frac{2}{\pi}. \]

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