Civil Engineering Reference
In-Depth Information
y=f(x)
y
4
y
n-1
y
3
y
n
y
n+1
y
2
y
1
A
1
A
2
A
3
A
n-1
A
n
x
x=a
x
i
x=b
∆x
∆x
∆x
∆x
∆x
Figure 3.1.
Trapezoidal rule.
b
=
()
=++++
∫
Af xdxAAA A
1
2
3
n
a
b
∆
x
(
)
=
()
=
∫
Af xdx
y
++++ +
22 2
y
y
yy
1
2
3
n
n
+
1
2
a
∆
x
n
∑
A
=
y
+
2
y
+
y
1
i
n
+
1
2
i
=
2
Example 3.1
Trapezoidal rule
Determine the area under the curve from 0 to
p
for
y=sin
(
x
) using the
trapezoidal rule with 2 and 4 strips.
∆
2
x
n
∑
A
=
y
+
2
y
+
y
1
i
n
+
1
i
=
2
Two strips are shown in Table 3.1:
Table 3.1.
Example 3.1 Trapezoidal rule
p
x
0
p/2
x
0
1.5708
3.1416
y=sin(x)
0
1
1.23E-16
p p
4
0210
2
(
)
==
A
=+
()
+
1 5708
.
