Chapter 07.03 Simpson's 1/3 Rule for Integration-More Examples ...

07.03.2 Chapter 07.02
2
2.8280
f 2.8280 e
4
3.362710
b a
a b
erfc0
.6560
f a
4 f f b
6
2
0.6560 5
f
5 4 f 2.8280
f 0.6560
6
4.3440
11
4
1.388810
43.3627
10
0.65029
6
0.47178
b) The exact value of the above integral cannot be found. For calculating the true error and
relative true error, we assume the value obtained by adaptive numerical integration using
Maple as the exact value.
0.6560
.6560
e
5
2
z
erfc 0 dz
0.31333
so the true error is
True Value Approximate Value
E t
0.31333
0.47178
0.15846
c) The absolute relative true error,
t
, would then be
True Error
t
100
True Value
0.15846
100
0.31333
50.573 %
Example 2
The concentration of benzene at a critical location is given by
where
c 1.75 erfc
erfc
x
x
e
32.73
0.6560
e erfc5.758
2
z
dz
So in the above formula
Since
erfc
2
z
0.6560
2
z
0.6560
e dz
e decays rapidly as z , we will approximate