What is the average value of (1)/(x) on the interval 4leqslant xleqslant 8

Question

Answer 1

To find the average value of the function \( f(x) = \frac{1}{x} \) on the interval

, we use the formula for the average value of a continuous function over an interval

:

In this case, \( f(x) = \frac{1}{x} \),

, and

. So, we need to compute the integral:

The antiderivative of

is

. Therefore,

Now, we can find the average value:

Thus, the average value of

on the interval

is:

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