Question

What is the average value of a function `y=7 sin x` on the interval `[0,pi]`?

Answer 1

The answer is `=14/pi`

Explanation:

The average value of a function `y=f(x)` from `x=a` to `x=b` is

`bary=(int_a^bf(x)dx)/(b-a)`

Therefore,

`bary=(int_0^(pi)7sinxdx)/(pi-0)`

`=7/pi[-cosx]_0^pi`

`=7/pi[1+1]`

`=14/pi`