Answer
\[\int_{0}^{\pi }{\cos x}dx=0\]
Work Step by Step
\[\begin{align}
& \int_{0}^{\pi }{\cos x}dx \\
& \text{From the graph we can see that the function }\cos x\text{ is odd about} \\
& x=\frac{\pi }{2},\text{ using the translation, we can express }\int_{0}^{\pi }{\cos x}dx\text{ as} \\
& \int_{0}^{\pi }{\cos x}dx=\int_{-\pi /2}^{\pi /2}{\cos \left( x+\frac{\pi }{2} \right)}dx \\
& \text{Using the theorem 5}\text{.4} \\
& \text{If }f\left( x \right)\text{ is odd, }\int_{-a}^{a}{f\left( x \right)dx}=0,\text{ then} \\
& \int_{0}^{\pi }{\cos x}dx=0 \\
\end{align}\]
