Chapter 14.2, Problem 62ES

The average value or mean value of a continuous function $f(x,y)$ over a region R in the $xy\text{-plane}$ is defined as $f_{ave}=\frac{1}{A(R)}{\displaystyle \underset{R}{\iint }f(x,y)dA}$ where $A(R)$ is the area of region R (compare to the definition preceding Exercise 35 in Section 14.1). Use this definition in these exercises.

Find the average value of $f(x,y)=x^2-xy$ over the region enclosed by $y=x$ and $y=3x-x^2.$