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