Calculus: the average of sinx, 0 to pi

Tutoring calculus, average values come up. The tutor mentions an example.

In calculus, the average value of a function f(x) over a given interval (a,b) is sometimes defined as ∫_a^bf(x)/(b-a). That is, it’s the integral of the function over that interval divided by the interval’s length.

For sinx, its integral is -cosx +C. The definite integral from 0 to pi would then be -(-1 – 1) = 2. Therefore, the average value of sinx from 0 to pi would be 2/π or approx. 0.6366.

Source:

Larson, Roland E. and Robert P. Hostetler. Calculus, part one, third edition. Toronto: D. C. Heath and Company, 1989.