Answer
1
Work Step by Step
see definition on p.281.
Average value =$\displaystyle \frac{1}{b-a}\int_{a}^{b}f(x)dx$
Using the given data,
Average value =$\displaystyle \frac{1}{4-2}\int_{2}^{4}\frac{8}{x^{2}}dx$
$=\displaystyle \frac{1}{2}\cdot 8\int_{2}^{4}x^{-2}dx=\qquad$ ...Power rule
$=4\cdot\left[\dfrac{x^{-1}}{-1}\right]_{2}^{4}$
$=4(-\displaystyle \frac{1}{4}+\frac{1}{2})$
$=1$
