Chapter 5.8, Problem 22ES

True-False Determine whether the statement is true or false. Explain your answer. (Assume that $f$ and $g$ denote continuous functions on an interval $\left[a,b\right]$ and that $f_{\text{ave}}$ and $g_{\text{ave}}$ denote the respective average values of $f$ and $g$ on $\left[a,b\right]$ .)

The average of the product of two functions on an interval is the product of the average values of the two functions on the interval; that is,

${\left(f\cdot g\right)}_{\text{ave}}=f_{\text{ave}}\cdot g_{\text{ave}}$