Question

Let g(x)=f(2x). Show that the average value of f on the interval [0,2b] is the same as the average value of g on the interval [0,b].

Please explain how this problem is done!!!

Answer 1

(1/(2b)) int 0 to 2b f(x) dx
?
(1/b) int 0 to b g(x) dx
= (1/b) int 0 to b f(2x) dx
let z = 2x then dx = dz/2
dx from 0 to b is dz from 0 to 2b
so
= (1/(2b)) int 0 to 2b f(z) dz done