Answer
$$\int\cos(\pi t/2)dt=\frac{2}{\pi}\sin(\pi t/2)+C$$
Work Step by Step
$$A=\int\cos(\pi t/2)dt$$
Let $u=\frac{\pi t}{2}$
Then $du=\frac{\pi}{2}dt$. So $dt=\frac{2}{\pi}du$
Substitute into $A$, we have $$A=\int\cos u(\frac{2}{\pi})du$$ $$A=\frac{2}{\pi}\int\cos udu$$ $$A=\frac{2}{\pi}(\sin u)+C$$ $$A=\frac{2}{\pi}\sin(\pi t/2)+C$$
