Question

What is the average value of a function `f(x) x^2 - 2x + 5` on the interval [2,6]?

Answer 1

`k=172/12`

Explanation:

`"let's recall that the average value of a function for an interval"`
`" of (a,b) is given by formula:"`
`k=1/(b-a)int_a^b f(x) d x`
`where;`
`k:"average value"`
`k=1/(6-2)int_2^6(x^2-2x+5)d x`

`k=1/4(|x^3/3-2x^2/2+5x |_2^6)`

`k=1/4(|x^3/3-x^2+5x|_2^6)`

`k=1/4[(6^3/3-6^2+5*6)-(2^3/3-2^2+5*2)]`

`k=1/4[(216/3-36+30)-(8/3-4+10)]`

`k=1/4[(216/3-6)-(8/3+6)]`

`k=1/4[(216-18)/3-(8+18)/3]`

`k=1/4[198/3-26/3]`

`k=1/4[172/3]`

`k=172/12`