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

Question

asked Oct 20, 2019 117k views

1 Answer

Andrey Tserkus · Answer 1 · 2019-10-25T06:54:05+0000

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