# Average Value of a Function

1. Jun 13, 2013

### Justabeginner

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. Jun 13, 2013

### Mandelbroth

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?

3. Jun 13, 2013

### Justabeginner

Yes, that is exactly what I have written on my paper here. Thank you so much for your help :)

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