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

Since the function is odd, we know that the average value over a symmetric interval is 0. Therefore, the average value of the function over $[- \pi, \pi]$ is 0.

Find the Average Value of the Function f(x)f ( x )f(x)

Find the Average Value of the Function $f ( x )$