Answer
$\frac{4}{\pi}$
Work Step by Step
Given
$$ f(t)= \sec^2 t,\ \ \ \ t\in [0,\pi/4]$$
Then
\begin{aligned}
f_{\mathrm{ave}}&=\frac{1}{b-a} \int_a^b f(t) d t\\
&=\frac{1}{\pi / 4-0} \int_0^{\pi / 4} \sec ^2 t d t\\
&=\frac{4}{\pi}[\tan t]_0^{\pi / 4}\\
&=\frac{4}{\pi}(1-0)\\
&=\frac{4}{\pi}
\end{aligned}
