6.5 Average Value of a Function/1

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

Failed to parse (syntax error): {\displaystyle f(x) = 4x-x^2, & nbsp(0, 4) }

${\begin{aligned}f_{avg}&={\frac {1}{4}}\int _{0}^{4}(4x-x^{2})dx\\[2ex]&={\frac {1}{4}}\left[{\bigg (}4x-{\frac {x^{3}}{3}}{\bigg )}\right]={\frac {1}{4}}{\bigg (}8-{\frac {8}{3}}{\bigg )}\\[2ex]&={\frac {1}{4}}[{\frac {32}{4}}]\\[2ex]&=38{\frac {1}{3}}\end{aligned}}$