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Compute the integral from 0 to (π/3) of cos (x/2)

by RoRi

Compute the following integral:

    \[ \int_0^{\frac{\pi}{3}} \cos \frac{x}{2} \, dx. \]

We compute as follows (using expansion/contraction of the interval of integration from Theorem 1.19 in Apostol):

    \begin{align*} \int_0^{\frac{\pi}{3}} \cos \frac{x}{2} \, dx &= 2 \int_0^{\frac{\pi}{6}} \cos x \, dx \\ &= 2\left( \sin \frac{\pi}{6} \right) \\ &= 1. \end{align*}

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