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E-35
Tips on Improving Integration Value Accuracy
•When a periodic function or integration interval results in positive
and negative f(x) function values
Perform separate integrations for each cycle, or for the positive
part and the negative part, and then combine the results.
Positive Part Negative Part
(
S Positive) (S Negative)
•When integration values fluctuate widely due to minute shifts in
the integration interval
Divide the integration interval into multiple parts (in a way that
breaks areas of wide fluctuation into small parts), perform
integration on each part, and then combine the results.
Appendix
<#031> ∫(ln(x), 1, e) = 1 (tol specification omitted.)
<#032>
∫
(
, 1, 5, 1×10
–7
)
= 0.8
a
b
f(x)dx =
a
x
1
f(x)dx +
x
1
x
2
f(x)dx +
.....+
x
4
b
f(x)dx
∫∫∫
∫
∫∫ ∫
a
b
f(x)dx =
a
c
f(x)dx + (–
c
b
f(x)dx)
1
x
2
S Negative
S Positive