what is the average value of f(x)=(x-3)^2 on the intergral [2,5]

Question

f(x)=(x-3)^2, [2,5].

 

Answer 1

The average value of a function is found by taking the integral of the function determining

the value of the integral and dividing by the difference of the range over which the function is acted upon.

1/(b-a) integral from 2 to 5 of (x-3)^2dx

f(x) = (x-3)^2

f(x) = x^2+9-6x

[2,5]

a = 2, b = 5.

The integral of the function

There fore