Chapter 5.1, Problem 8E

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.

8. The depth of a 3-ft by 3-ft hole in the ground, measured at 1—ft intervals, is given in the following table.

a. Estimate the volume of the hole by using a Riemann sum with m =n = 3 and the sample points to be the upper left conwrs of the subsquares of R.

b. Find the average depth of the hole.

y

x	0	1	2	3
0	6	6.5	6.4	6
1	6.5	7	7.5	6.5
2	6.5	6.7	6.5	6
3	6	6.5	5	5.6