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.)
f(x) = 8 cos(x),
(0, π/6)
Integrate and then divide by the length of the path i.e. find [tex]\frac{6}{\pi}\int_0^{\frac{\pi}{6}} 8 \cos(x)dx[/tex] [tex]\frac{48}{\pi}\int_0^{\frac{\pi}{6}} \cos(x)dx
\\
\\ \frac{48}{\pi}\sin{x}|_0^ \frac{\pi}{6}
\\
\\ \frac{48}{\pi}(\sin{\frac{\pi}{6}}-\sin{0})
\\
\\ \frac{48}{\pi}( \frac{1}{2}-0)
\\
\\ \frac{48}{\pi}\times \frac{1}{2}
\\
\\ \frac{24}{\pi}[/tex]
