James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

998 Chapter 15 Multiple Integrals
where AsRd − 388 ? 276. To estimate the value of this double integral, let’s use the
Midpoint Rule with m − n − 4. In other words, we divide R into 16 subrectangles of
equal size, as in Figure 19. The area of each subrectangle is
DA − 1
16 s388ds276d − 6693 mi2 12
y
276
40 36
44 32
28
24
12
16
20
16
40
36
32
12
28
0
24
4 8 12 16
20
32
28
24
8
FIGURE 19
0
388
x
Using the contour map to estimate the value of f at the center of each subrect angle,
we get
yy f sx, yd dA < o 4
o 4
f sx i , y j d DA
i−1 j−1
R
< DAf0 1 15 1 8 1 7 1 2 1 25 1 18.5 1 11
1 4.5 1 28 1 17 1 13.5 1 12 1 15 1 17.5 1 13g
− s6693ds207d
Therefore
f ave < s6693ds207d
s388ds276d
< 12.9
On December 20–21, 2006, Colorado received an average of approximately 13 inches
of snow.
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