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Compute the integral from 0 to π of (1/2 + cos t)

Compute the following integral:

    \[ \int_0^{\pi} \left( \frac{1}{2} \, dt + \cos t \right) \, dt. \]


We compute as follows:

    \begin{align*}  \int_0^{\pi} \left( \frac{1}{2} + \cos t \right) \, dt &= \int_0^{\pi} \frac{1}{2} + \int_0^{\pi} \cos t \, dt \\  &= \left. \frac{t}{2} \right|_0^{\pi} + \sin t \biggr \rvert_0^{\pi} \\  &= \frac{\pi}{2}. \end{align*}

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