Graphics Programs Reference
In-Depth Information
where x i and A i are giveninTable 6.6. The sum isevaluatedinthe following table:
x i
cos
π
x i
A i
A i cos
π
x i
0
.
041 448
0
.
991 5340
.
383 464
0
.
380 218
0
.
245 275
0
.
717 525
0
.
386 875
0
.
277 592
0
.
556 165
0
.
175 533
0
.
190435
0
.
033 428
0
.
848 982
0
.
889 5500
.
039 225
0
.
034 892
=
0
.
589 490
Thus
1
cos
π
x ln x dx
0
.
589 490
0
The second integral isfree of singularities, so that itcan beevaluatedwith Gauss-
=
4, wehave
1
4
cos
π
x ln x dx
0
.
25
A i cos
π
x i ln x i
0
.
5
i
=
1
where the nodal abscissas are (see Eq. (6.28))
1
+
0
.
5
1
0
.
5
x i =
+
ξ i =
0
.
75
+
0
.
25
ξ i
2
2
Looking up
ξ i and A i in Table 6.3 leads to the following computations:
ξ i
x i
cos
π
x i ln x i
A i
A i cos
π
x i ln x i
0
.
861 136
0
.
534 716
0
.
068 141
0
.
347 855
0
.
023 703
0
.
339 981
0
.
665 005
0
.
202 133
0
.
652 145
0
.
131 820
0
.
339 981
0
.
834 995
0
.
156 638
0
.
652 145
0
.
102 151
0
.
861 136
0
.
965 284
0
.
035 123
0
.
347 855
0
.
012 218
=
0
.
269 892
fromwhich
1
π
.
.
=
.
cos
x ln x dx 0
25(0
269 892)
0
067 473
0
.
5
Therefore,
1
cos
π
x ln x dx
0
.
589 490
0
.
067 473
=−
0
.
656 96 3
0
which iscorrect to six decimal places.
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