How do you find the average value of the function for f(x)=x+sinx, 0<=x<=2pi?

1 Answer
Jun 13, 2018

The average value is pi.

Explanation:

The average value of a function continuous on [a, b] is given by

A = 1/(b - a) int_a^b f(x) dx

Thus

A = 1/(2pi - 0) int_0^(2pi) x + sinx

A = 1/(2pi) [1/2x^2 - cosx]_0^(2pi)

A = 1/(2pi)(1/2(4pi^2) - 1 + cos(0))

A = 1/(4pi)(4pi^2)

A = pi

Hence, the average value of the given function on the interval 0 ≤ x ≤ 2pi is pi.

Hopefully this helps!