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
Explanation:
The average value of a function continuous on
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
Hopefully this helps!