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Average Value of a Function

  1. Jun 13, 2013 #1
    1. The problem statement, all variables and given/known data
    What is the average value of a function 1/x between x=2/3 and x=8/3?


    2. Relevant equations
    1/(b-a) ∫f(x) dx with a and b being the lower and upper limits, respectively


    3. The attempt at a solution

    1/([8/3] - [2/3])∫1/x dx
    1/(6/3) ∫1/x dx
    1/2 ∫1/x dx
    1/2 * (ln x)

    Plug in:
    (ln {8/3})/2 - (ln {2/3}/2)
    ln 4/2
    ln 2

    Is this correct? Thanks :)
     
  2. jcsd
  3. Jun 13, 2013 #2
    Looks good.

    Though, just to be clear, your reasoning for your last few steps was ##\frac{1}{2}\ln\left(\frac{(\frac{8}{3})}{(\frac{2}{3})}\right) = \frac{1}{2}\ln(4) = \ln(4^{\frac{1}{2}}) = \ln2##, correct?
     
  4. Jun 13, 2013 #3
    Yes, that is exactly what I have written on my paper here. Thank you so much for your help :)
     
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