Question

Find the average value of the function on the given interval?

Answer 1

`f(x)_(avg)=8/3`

OR

`f(x)_(avg)=2.66`

Explanation:

The average value of a function `=(int_a^bf(x)dx)/(b-a)`

Here `f(x)=4x-x^2` and `b=4` , `a=0`

So,

`f(x)_(avg)=(int_0^4(4x-x^2)dx)/(4-0)`

`f(x)_(avg)=[(4x^2)/2-x^3/3]_0^4/4`

`f(x)_(avg)=[2x^2-x^3/3]_0^4/4`

`f(x)_(avg)=((2xx4^2-4^3/3)-(2xx0^2-0^3/3))/4`

`f(x)_(avg)=(32/3)/4`

`f(x)_(avg)=8/3`

`f(x)_(avg)=2.66`