What is the average value of a function #sinx# on the interval #[0, pi/3]#? Calculus Applications of Definite Integrals The Average Value of a Function 1 Answer ali ergin May 3, 2016 #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)# Answer link Related questions The profit (in dollars) from the sale of x lawn mowers is ... What is the average value of the function #f(x)=(x-1)^2# on the interval from x=1 to x=5? What is the average value of the function #u(x) = 10xsin(x^2)# on the interval #[0,sqrt pi]#? What is the average value of the function #f(x)=cos(x/2) # on the interval #[-4,0]#? What is the average value of the function #f(x) = x^2# on the interval #[0,3]#? What is the average value of the function #f(t)=te^(-t^2 )# on the interval #[0,5]#? What is the average value of the function #f(x) = x - (x^2) # on the interval #[0,2]#? What is the average value of the function #f(t) = t (sqrt (1 + t^2) )# on the interval #[0,5]#? What is the average value of the function #f(x) = sec x tan x# on the interval #[0,pi/4]#? What is the average value of the function #f(x) = 2x^3(1+x^2)^4# on the interval #[0,2]#? See all questions in The Average Value of a Function Impact of this question 3065 views around the world You can reuse this answer Creative Commons License