Answer
\[\frac{{\sqrt 2 }}{4}\]
Work Step by Step
\[\begin{gathered}
\int_0^{\pi /8} {\cos 2x} dx \hfill \\
\hfill \\
{\text{integrating}} \hfill \\
\hfill \\
\frac{1}{2}\left[ {\sin 2x} \right]_0^{\pi /8} \hfill \\
\hfill \\
{\text{Use the fundamental theorem of calculus}} \hfill \\
\hfill \\
= \frac{1}{2}\left[ {\sin 2\left( {\frac{\pi }{8}} \right) - \sin \left( 0 \right)} \right] \hfill \\
\hfill \\
{\text{Simplify}} \hfill \\
\hfill \\
= \frac{1}{2}\left( {\frac{{\sqrt 2 }}{2}} \right) \hfill \\
\hfill \\
\frac{{\sqrt 2 }}{4} \hfill \\
\end{gathered} \]
