What's the average of this function

If f(x) = sin(x) for all x, then the average value of 'f' in the interval [0, π] is

A) 1/2

B) 1/π

C) π/2

D) 2/π

Thank you.

The average value is the integral of the function divided by the length of the interval.

π
∫ sin(x) dx = -cos(x) {evaluate at π and 0} = -cos(π) + cos(0) = 2.
0

The interval is of length π, so the answer is D) 2/π.

the formula for avg value over an interval is :


1 b
------∫ f(x)
b-a a

this is
1 π
----∫ sin(x)=1/π*-[cos(π)-cos(0)]
π 0

=1/π*-[-1-1]
=1/π*-[-2]
=2/π