Question

What is the average value of the function `f(x)=(x-1)^2` on the interval `[1,5]`?

Answer 1

`16/3`

Explanation:

`f(x)=(x-1)^2=x^2-2x+1`

`"Average of all points of"` `f(x)in[a,b]=(int_a^bf(x)dx)/(b-a)`

`int_1^5(x^2-2x+1)dx=[x^3/3-x^2+x]_1^5=[5^3/3-5^2+5]-[1/3-1+1]=65/3-1/3=64/3`

`(64/3)/4=16/3`