Find the average value of the function $f(x)$ in the interval $[-\pi, \pi]$ . $f(x)=\sin ^{6} x \cos ^{5} x$
A) $\pi$
B) 0
C) $\frac{\pi}{5}$
D) $\frac{\pi}{12}$
E) $\frac{\pi}{6}$

Question

Quizplus · Accepted Answer

The function $f(x) = \sin^6 x \cos^5 x$ is an odd function because it is the product of an even power of $\sin x$ and an odd power of $\cos x$. The average value of an odd function over a symmetric interval around zero is zero.

Find the Average Value of the Function f(x)f(x)f(x) In the Interval [−π,π][-\pi, \pi][−π,π]

Find the Average Value of the Function $f(x)$ In the Interval $[-\pi, \pi]$