`h(x) = cos^4(x) sin(x), [0, pi]` Find the average value of the function on the given interval.

The average value is the integral of a function over an interval divided by the length of an interval. The length here is `pi,` found the integral.

Find the indefinite integral first, for this make a substitution `u=cos(x),` then `du = -sin(x) dx.`

`int cos^4(x)sin(x) dx = -int u^4 du = -1/5 u^5 +C = -1/5 cos^5(x) +C.`

So the definite integral is

`-1/5 cos^5(x)|_(x=0)^pi = -1/5(-1-1)= 2/5.`

And the average value is `2/(5pi) approx 0.127.`