Chapter 5 - Applications of Integration - 5.5 Average Value of a Function - 5.5 Exercises - Page 391: 3

$f_{avg}=\frac{6}{\pi}$

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, $f_{avg}=\frac{6}{\pi}$