Question

How do you find the average value of the function for `f(x)=x^3, 0<=x<=2`?

Answer 1

`2`

Explanation:

The average value is basically the area under the curve divided by the length of the base, i.e.:

`1/(color(blue)(2)-color(blue)(0)) int_color(blue)(0)^color(blue)(2) \ x^3 \ dx = 1/2 [ 1/4 x^4 ]_color(blue)(0)^color(blue)(2) = 1/8((color(blue)(2))^4 - (color(blue)(0))^4) = 1/8(16-0) = 2`