Question

Find the average of the function over the given interval and all values of x in the interval for which the function equals its average value. (Round your answer to three decimal places.) @electrokid

Answer 1

what formula did you use?

Answer 2

for what values of "x" is f(x)=average of f(x)

Answer 3

\[\Large{
f(x)=\frac{\int_0^{\pi/2}7\cos(x)dx}{\int_0^{\pi/2}dx}\\
\cancel{7}\cos(x)=\frac{\cancel{7}[\sin(x)]_0^{\pi/2}}{[x]_0^{\pi/2}}\\
\cos(x)=\frac{\sin(\pi/2)-\sin(0)}{{\pi\over2}-0}={2\over\pi}\\
\boxed{x=\cos^{-1}\left(2\over\pi\right)}
}\]

Answer 4

you can use a calculator to find this "x" value to "3" decimal places
and find the corresponding "y"

Answer 5

sorry @electrokid had to go to class but thank you for your help again im going to try working out the problem now.