$12.27 \int_{0}^{\pi} \cos ^{2} x d x$
12.27 To transform the integrand, we will use the power reduction formula (4.17). Then we get

$$
\begin{aligned}
& \int_{0}^{\pi} \cos ^{2} x d x=\int_{0}^{\pi} \frac{1+\cos 2 x}{2} d x=\frac{1}{2}\left(\int_{0}^{\pi} d x+\int_{0}^{\pi} \cos 2 x d x\right)= \\
& =\frac{1}{2}\left(\left.x\right|_{0} ^{\pi}+\left.\frac{1}{2} \sin 2 x\right|_{0} ^{\pi}\right)=\frac{1}{2}\left(\pi-0+\frac{1}{2} \cdot 0\right)=\frac{\pi}{2}
\end{aligned}
$$

Answer: $\frac{\pi}{2}$.