07.04.1
Multiple-Choice Test
Chapter 07.04
Romberg Rule
1.
If
n
I
is the value of integral
( )
∫
b
a
dx
x
f
using
n
-segment trapezoidal rule, a better
estimate of the integral can be found using Richardson’s extrapolation as
(A)
15
2
2
n
n
n
I
I
I
−
+
(B)
3
2
2
n
n
n
I
I
I
−
+
(C)
n
I
2
(D)
n
n
n
n
I
I
I
I
2
2
2
−
+
2.
The estimate of an integral of
( )
∫
19
3
dx
x
f
is given as 1860.9 using 1-segment
trapezoidal rule.
Given
( )
27
.
20
7
=
f
,
( )
125
.
45
11
=
f
, and
( )
23
.
82
14
=
f
, the value
of the integral using 2-segment trapezoidal rule would most nearly be
(A)
787.32
(B)
1072.0
(C)
1144.9
(D)
1291.5
3.
The value of an integral
( )
∫
b
a
dx
x
f
given using 1, 2, and 4 segments trapezoidal rule is
given as 5.3460, 2.7708, and 1.7536, respectively.
The best estimate of the integral
you can find using Romberg integration is most nearly
(A)
1.3355
(B)
1.3813
(C)
1.4145
(D)
1.9124

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