Chapter 5.1, Problem 10E

In the following exercises, estimate the volume of the solid under the surface z= f(x. y) and above the rectangular

legion R by using a Riemann sum with m = n = 2 and the sample points to be the lower left corners of the subrectangles of the partition.

10. The level curves f(x. y) = k given in the following graph, where

a. Apply the midpoint rule with m=n=2 to estimate the double integral ${\displaystyle \underset{R}{\int }f\left(x,y\right)dA}$ , where $R=\left[0,1,0.5\right]\times \left[0,1,0.5\right]$

b. Estimate the average value of the function f on R.