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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!!!

  • calculus -

    (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
    = (1/(2b)) int 0 to 2b f(z) dz done

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