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Math Help - Average value of function

  1. #1
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    Average value of function

    Hi, I was wondering if anyone can help:

    Find a positive value of k such that the average value of f(x) = 1/ (kx^2) over the interval [k,1] is 2.

    Thanks,
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  2. #2
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    Quote Originally Posted by Wintaker99 View Post
    Hi, I was wondering if anyone can help:

    Find a positive value of k such that the average value of f(x) = 1/ (kx^2) over the interval [k,1] is 2.

    Thanks,
    The average of f(x) over [k,1] is:

    Av(f) = [integral_{x=k to 1} f(x) dx]/(1-k) = [(1-k)/k^2]/(1-k) = 1/k^2,

    so if Av(f) = 2, we have 1/k^2=2, and so k=1/sqrt(2).

    RonL
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