E-22
• A smaller
tol
value increases precision, but it also increases calculation time. When
specifying
tol
, use value that is 1
×
10
–14
or greater.
Precautions for Integration Calculation Only
• Integration normally requires considerable time to perform.
• For
f
(
x
)
0 where
a
x
b
(as in the case of
∫
0
1
3
x
2
– 2 = –1), calculation will produce a
negative result.
• Depending on the content of
f
(
x
) and the region of integration, calculation error that
exceeds the tolerance may be generated, causing the calculator to display an error
message.
Precautions for Differential Calculation Only
• If convergence to a solution cannot be found when
tol
input is omitted, the
tol
value will
be adjusted automatically to determine the solution.
• Non-consecutive points, abrupt fluctuation, extremely large or small points, inflection
points, and the inclusion of points that cannot be differentiated, or a differential point or
differential calculation result that approaches zero can cause poor precision or error.
A
Tips for Successful Integration Calculations
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.
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.
S Positive
S Negative
∫∫
a
c
f(x)dx + (–
c
b
f(x)dx)
Positive Part
(
S Positive)
Negative Part
(S Negative)
b
a
x
1
x
2
x
3
x
4
x
0
f (x)
a
b
f(x)dx =
a
x
1
f(x)dx +
x1
x
2
f(x)dx +
.....
∫∫∫
x4
b
f(x)dx
∫
+
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