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

by RoRi

August 4, 2015

Compute the following integral:

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

We compute as follows:

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

Stumbling Robot

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

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