Chapter 16.2, Problem 95E

Average value Use the definition for the average value of a function over a region R(Section 16.1), $\bar{f}=\frac{1}{\text{area}\text{of }R}{\displaystyle \int {\displaystyle {\int }_{R}f(x,y)dA}}$.

95. Find the average value of a – x − y over the region $R=\{(x,y):x+y\le a,x\ge 0,y\ge 0\}$, where a > 0