Chapter 16.2, Problem 96E

Average value Use the definition for the average value of a function over a region R(Section 16.1)

$\bar{f}=\frac{1}{\text{area}\text{of}R}{\displaystyle \int {\displaystyle {\int }_{R}f(x,y)dA.}}$

96. Find the average value of z = a² − x² − y² over the region $R=\{(x,y):x^2+y^2\le a^2\},$where a > 0