Find the average value of the function on the given interval. f(x)=9cosx ,[0,pi/2]

To determine the average value of the given function,
we'll have to compute the definite integral of the function over the interval [0 ,
pi/2].

f avg. = Int f(x)dx/(b-a), where the interval is
[a,b]

To calculate the definite integral, we'll apply
Leibniz-Newton formula, over the interval [a,b]:

Int f(x) =
F(b) - F(a)

f avg. = Int 9cosx dx/(pi/2 -
0)

f avg. = 9*Int cosx
dx/(pi/2)

f avg. = 9*(sinpi/2-
sin0)/(pi/2)

f avg. =
9*(1-0)/(pi/2)

f avg. =
18/pi

The requested average value of the
function is f avg. = 18/pi.