$\int\limits_0^{\pi /2} {\cos 2x} \,dx$

$\int\limits_0^{\pi /2} {\cos 2x} \,dx = \left[ {\cfrac{1}{2}\sin 2x} \right]_0^{\pi /2}$

$= \cfrac{1}{2}\left( {\sin \pi - \sin 0} \right) = \cfrac{1}{2}\left( {0 - 0} \right) = 0$