What is the average value of 8-2x^3 on the interval [2,4]

Question

Answer 1

To find the average value of the function \( f(x) = 8 - 2x^3 \) on the interval

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

:

Here,

and

. So, we need to compute:

First, we find the integral:

We can split this into two separate integrals:

Evaluate each integral separately:

Now, combine the results:

Finally, compute the average value:

Thus, the average value of

on the interval

is

.

Вопрос