Question

How do you find the average value of: `f(x) = 8 sin x + 6 cos x` on the interval `[0,(10pi)/6 ]`?

Answer 1

The average value of a function `f` on an interval `[a, b]` is found by:
evaluate `int_a^b f(x) dx` then divide by the length of the interval, `b-a`

So, find `int_0^((10 pi)/6) (8sinx + 6 cosx) dx`.

Then divide that number by `(10 pi)/6` (or. better yet, divide by `(5 pi)/3`)