Answer
$f_{avg}=\frac{6}{\pi}$
Work Step by Step
Given: Average value of the function $f(x)=3cosx$ over the interval $[-\pi/2,\pi/2]$ is given by
Average value of the function $f(x)$ over the interval $[a.b]$ is given by
$f_{avg}=\frac{1}{b-a}\int_{a}^{b}f(x)dx$
$f_{avg}=\frac{1}{-\pi/2-(-\pi/2)}\int_{-\pi/2}^{\pi/2}3cosxdx$
$=\frac{1}{\pi}[3sinx]_{-\pi/2}^{\pi/2}$
Hence, $f_{avg}=\frac{6}{\pi}$