Answer
$\dfrac{2}{\pi} $
Work Step by Step
We need to use the fundamental Theorem of calculus. $\overline{f}=\dfrac{1}{b-a}\int_a^b f(x) dx $
Now, $\overline{f}=\dfrac{1}{\dfrac{\pi}{4}-0}\int_0^{\pi/4} \cos (2x) dx\\=\dfrac{4}{\pi}[\dfrac{\sin 2x}{2} ]_0^{\pi/4} \\=\dfrac{2}{\pi}[\sin (\pi/2)-\sin (0) ]\\=\dfrac{2}{\pi}[1-0]\\=\dfrac{2}{\pi} $
