Answer
$2.215$
Work Step by Step
We are given that $f(x)=|2x-5|$, interval $[0,4]$
Apply formula: $\overline{f}=\dfrac{1}{b-a}\int_a^b f(x) \ dx$
So, we have: $\overline{f}=\dfrac{1}{4-0}\int_{0}^4 |2x-5| \ dx=\dfrac{1}{4} \int_{0}^4 |2x-5| \ dx$
Apply formula: $\int |px+q| \ dx=\dfrac{1}{2p} (px+q)|px+q|+C$
So, we can write as: $\overline{f}=\dfrac{1}{4}[\dfrac{1}{(2)(2)}(2x-5)|2x-5|]_0^4$
or, $=\dfrac{1}{16}[(2x-5)|2x-5|]_0^4$
or, $=\dfrac{1}{16}[(3)|3|]-\dfrac{1}{16}[(-5)|-5|]$
Thus, $ \overline{f} \approx 2.215$
