Find the average value of the function g(x) =
"\frac{lnx}{x}" alt="\frac{lnx}{x}" align="absmiddle" class="latex-formula"> over the interval [1, e].
1 answer:
Answer:

Step-by-step explanation:
<u>Average Value of a Function</u>
Given a function g(x), we can compute the average value of g in a given interval (a,b) with the equation:

We use the given data

We now compute the indefinite integral with a u-substitution

We'll use the substitution u=lnx, du=dx/x. Then

Integrating

Since u=lnx

The average value is


Since lne=1, and ln1=0


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