(LineI/LineO)
5() 32
2
2×3 =3 2= 4.242640687...
(MathI/MathO)
23
3
2
(LineI/LineO)
23
4.242640687
, , : These functions use Gauss-Kronrod methods to perform
numerical integration, approximation of the derivative based on central
difference method, and calculation of the sum of a specific range of f(x).
Input Syntax
(1) When MathI/MathO or MathI/DecimalO is selected
(2) When LineI/LineO or LineI/DecimalO is selected
*
1
*
2
*
3
(1)
∫
𝑎
𝑏
𝑓 𝑥 𝑑𝑥
𝑑
𝑑𝑥
𝑓 𝑥
𝑥=𝑎
∑
𝑥=𝑎
𝑏
𝑓 𝑥
(2)
∫
𝑓 𝑥 , 𝑎, 𝑏, 𝑡𝑜𝑙
𝑑
𝑑𝑥
𝑓 𝑥 , 𝑎, 𝑡𝑜𝑙
∑
𝑓 𝑥 ,𝑎,𝑏
*1 tol specifies tolerance, which becomes 1 × 10
-5
when nothing is input
for tol.
*2 tol specifies tolerance, which becomes 1 × 10
-10
when nothing is input
for tol.
*3 a and b are integers that can be specified within the range of -1 × 10
10
< a ≦ b < 1 × 10
10
.
Integration and Differential Calculation Precautions
• When using a trigonometric function in f(x), specify “Radian” as the angle
unit.
• A smaller tol value increases precision, but it also increases calculation
time. When specifying tol, use value that is 1 × 10
-14
or greater.
• Integration normally requires considerable time to perform.
• Depending on the content of f(x), positive and negative values within the
region of integration, or the region of integration, calculation error that
exceeds the allowable range may be generated, causing the calculator
to display an error message.
• With derivative calculations, 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 a differential
calculation result that approaches zero can cause poor precision or
error.
∫
1
𝑒
ln 𝑥 𝑑𝑥
(MathI/MathO)
(x)1(e)
1
(LineI/LineO)
(x)(,)
1(,)(e)
1
To obtain the derivative at point x = π/2 for the function y = sin(x) (Angle
Unit: Radian)
()(x) …(1)
(MathI/MathO)
(Continued following (1))
(π)2
0
(LineI/LineO)
(Continued following (1))
(,)(π)2
0
∑
𝑥=1
5
𝑥+1 = 20
15
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