The Formula for the Average Value of the function f(x) on the given interval [a,b] is
[tex] Avg=\frac{1}{b-a}\int\limits^a_b {f(x)} \, dx [/tex]
Thus the formula for the Average Value of the function [tex] f(x)=4x^4 [/tex] on the interval [2,5] is given by
[tex] Avg= \frac{1}{5-2}\int\limits^2_5 {4x^4\\} \, dx \\ =\frac{1}{3}4\frac{x^5}{5})_{2}^{5} [/tex]
[tex] =\frac{4124}{5} [/tex]
Thus the Average value of the function f(x)=4x^4 on the interval [2,5] is [tex] \frac{4124}{5} [/tex]
