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 |
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