Web Analytics
Answered

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)


...?

Verified Answer :

Integrate and then divide by the length of the path
i.e. find

\(\frac{6}{\pi}\int_0^{\frac{\pi}{6}} 8 \cos(x)dx\)

\(\frac{48}{\pi}\int_0^{\frac{\pi}{6}} \cos(x)dx \\ \\ \frac{48}{\pi}\sin{x}|_0^ \frac{\pi}{6} \\ \\ \frac{48}{\pi}(\sin{\frac{\pi}{6}}-\sin{0}) \\ \\ \frac{48}{\pi}( \frac{1}{2}-0) \\ \\ \frac{48}{\pi}\times \frac{1}{2} \\ \\ \frac{24}{\pi}\)

Related Questions