Civil Engineering Reference
In-Depth Information
x
= 0 to 8
∆
x
= 2 =
h
x
and
y
= 0 to 8
∆
y
= 2 =
h
y
hxhy
9
∑
∫∫
(
)
=
=
fxyV
,
Weighting operator:
14241
416816 4
28482
416816 4
14241
Solving for
z
:
xy
=
16
z
Table 3.15 shows the set up and summation as follows:
hxhy
∑
∫∫
(
)
=
=
fxyV
,
9
22
9
()
==
144
64
V
Table 3.15.
Example 3.6 Double integration by Simpson's
one-third rule
x
y
weight
f(x,y)
weight*f(x,y)
0
0
1
0
0
0
2
4
0
0
0
4
2
0
0
0
6
4
0
0
0
8
1
0
0
2
0
4
0
0
2
2
16
0.25
4
2
4
8
0.5
4
2
6
16
0.75
12
(
Continued
)
