Question

Find the average value of the function f ( x ) = 4 x 4 on the interval 2 ≤ x ≤ 5

Answer 1

The Formula for the Average Value of the function f(x) on the given interval [a,b] is

`Avg=(1)/(b-a)\int\limits^a_b {f(x)} \, dx`

Thus the formula for the Average Value of the function
`f(x)=4x^4` on the interval [2,5] is given by

`Avg= (1)/(5-2)\int\limits^2_5 {4x^4\\} \, dx \\ =(1)/(3)4(x^5)/(5))_(2)^(5)`

`=(4124)/(5)`

Thus the Average value of the function f(x)=4x^4 on the interval [2,5] is
`(4124)/(5)`