# How to evaluate the definite integral (0,1) ∫ cos(πt/2)dt ?

Set $u = \pi \cdot \frac{t}{2} \implies \mathrm{du} = \frac{\pi}{2} \mathrm{dt}$ and integration limits are
$t = 1 \implies u = \frac{\pi}{2}$ and $t = 0 \implies u = 0$ hence the integral becomes
${\int}_{0}^{\frac{\pi}{2}} \left(\frac{2}{\pi}\right) \cdot \cos u \mathrm{du} = \left(\frac{2}{\pi}\right) \cdot {\left[\sin\right]}_{0}^{\frac{\pi}{2}} = \frac{2}{\pi}$