Integration Calculations

Function for performing numerical integration using the Gauss-Kronrod method.
Natural Display input syntax is ∫^b_a f (x)dx, while Linear Display input syntax is ∫ (f (x), a, b, tol).

tol specifies tolerance, which becomes 1 × 10-5 when nothing is input for tol.

Example 1: ∫^e₁ ln(x) = 1

(MthIO-MathO)

(X)1(e)
1

(LineIO)

(X)(,) 1(,)(e)
1

Example 2: ∫(¹_x2 , 1, 5, 1 × 10-7) = 0.8 (LineIO)

1(X)(,) 1(,) 5(,)
17
0.8

Example 3: ∫^π₀ (sin x + cos x)2 dx = π (tol: Not specified) (MthIO-MathO) (Angle unit: Rad)

(X)(X)0
(π)
π

Integration Calculation Precautions

Integration calculation can be performed in the COMP Mode only.

The following cannot be used in f(x): Pol, Rec, ÷R. The following cannot be used in f(x), a, b, or tol: ∫, d/dx, Σ, Π.

When using a trigonometric function in f(x), specify Rad 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) and the region of integration, calculation error that exceeds the tolerance may be generated, causing the calculator to display an error message.

The content of f(x), positive/negative values within the integration interval, and the interval to be integrated can cause large error in the resulting integration values. (Examples: When there are parts with discontinuous points or abrupt change. When the integration interval is too wide.) In such cases dividing the integration interval into parts and performing the calculation may improve calculation accuracy.

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.

(1) Positive Part
(2) Negative Part

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.