If [math]f[/math] is integrable on [math][a,b][/math], then its [i]average value[/i] [i]on [/i][math][a,b][/math], also called its [i]mean[/i], is defined to be the definite integral of [math]f[/math] (with respect to [math]x[/math]) evaluated from [math]x=a[/math] to [math]x=b[/math], then divided by the quantity [math]b-a[/math]. [br][br]That is, [math]av(f) = \frac{1}{b-a} \int_a^b f(x)\;dx[/math].

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]