1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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 :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted