`f(x) = sin(4x), [-pi, pi]` Find the average value of the function on the given interval.

The average value on an interval is the integral on this interval divided by the length of the interval.

The length is 2pi. The integral is

`-1/4 cos(4x)|_(x=-pi)^(pi)=-1/4 (1-1)=0.`

So the average value is zero.

The average value on an interval is the integral on this interval divided by the length of the interval.

The length is 2pi. The integral is

`-1/4 cos(4x)|_(x=-pi)^(pi)=-1/4 (1-1)=0.`

So the average value is zero.