Question

What is the average value of a function `sinx` on the interval `[0, pi/3]`?

Answer 1

`k=3/(2pi)`

Explanation:

`k=1/(b-a) int_a^b f(x) d x`

`k=1/(pi/3) int_0^(pi/3) sin x d x`

`k=3/pi[|-cos x|_0^(pi/3)]`

`k=3/pi[-cos(pi/3)+cos 0]`

`k=3/pi[-1/2+1]`

`k=3/pi*1/2`

`k=3/(2pi)`