6.5 Average Value of a Function/1

\scriptstyle Find the average value of the function on the given interval.

$f(x)=4x-x^{2},(0,4)$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} f_{avg} &= \frac{1}{4} \int_{0}^{4} (4x-x^2) dx \\[2ex] &=\frac{1}{4} \left[\bigg( 4x-\frac{x^3}{3}\bigg) \right] = \frac{1}{4} \bigg(8-\frac{8}{3} \bigg) \\[2ex] &= \frac{1}{4}[\frac{32}{4}] \\[2ex] &= 38 \frac{1}{3} \end{align} }