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Homework Help: Average Value of a function

  1. Jul 24, 2011 #1
    1. The problem statement, all variables and given/known data

    If fave [a,b] denotes the average value of f on the interval [a,b] and a<c<b, show that
    fave[a,b] = (c-a)/(b-a) fave[a,c] + (b-c)(b-a) fave[c,b]

    2. Relevant equations

    All i know is the mean value theorem for integrals is f(c) = fave = 1/(b-a) integral(f(x),x,b,a)

    3. The attempt at a solution

    Tried using the theorem, but had no idea how to get to that point.

  2. jcsd
  3. Jul 24, 2011 #2

    Why don't you apply the definition of the fave to fave[a,c] and fave[c,b]?

    Once you do this, I think you'll see that your expression simplifies quite nicely.
  4. Jul 24, 2011 #3
    Hello, I tried it and i believe this is how it goes...

    fave[a,c] = 1/(c-a) [f(c)-f(a)]
    fave[c,b] = 1/(b-c) [f(b)-f(c)]

    then i add it together or what? Kind of confused on what to do because this gives something weird...

    I do know that u can split up the bounds from [a,c] and [c,b] to get [a,b].. does that correlate with what this gotta do?
  5. Jul 24, 2011 #4
    Perhaps I don't understand your notation, but shouldn't [f(c)-f(a)] be Int[f, a, c]?

    Try plugging in those expressions into the right-side of the equation that you're trying to prove.
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