Answer
$$\frac{2}{\pi}$$
Work Step by Step
By substitution:
Let $u = \frac{\pi}{2}t$. Hence, $du = \frac{\pi}{2}dt$.
Thus, substituting $\frac{\pi}{2}t$ with $u$ and $dt$ with $\frac{2}{\pi}du$:
$\int^1_0\cos({\frac{\pi}{2}t})dt$
$=\int^{\frac{\pi}{2}}_0\cos u (\frac{2}{\pi}du)$
$=\frac{2}{\pi}\int^{\frac{\pi}{2}}_0\cos u du$
$=\frac{2}{\pi}[\sin u]|^{\frac{\pi}{2}}_0$
$=\frac{2}{\pi}[\sin(\frac{\pi}{2})-\sin 0]$
$=\frac{2}{\pi}[1-0]$
$=\frac{2}{\pi}$
