Intg: Determines the largest integer that does not exceed a value. See

21.

Note: Using functions can slow down a calculation, which may delay display of the result. Do not perform any subsequent operation while waiting for the calculation result to appear. To interrupt an ongoing calculation before its result appears, press A.

Integration and Differential Calculation Precautions

•Integration and differential calculations can be performed in the COMP Mode (,1) 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 ⋅ 10–14or 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 ∫01 3x2 – 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.

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.

 

 

∫ b f(x)dx = ∫c f(x)dx + (–∫bf(x)dx)

 

 

 

 

a

 

a

 

c

 

S Positive

 

 

 

 

 

 

 

 

 

Positive Part

Negative Part

 

S Negative

 

(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.

f (x)

 

 

 

∫ b f(x)dx = ∫x1

f(x)dx + ∫x2 f(x)dx + .....

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a

a

x1

 

 

 

 

 

+ ∫ b

f(x)dx

 

 

 

 

 

x

x4

 

 

 

 

a x1 x2 x3 x4

 

 

 

0

 

b

 

 

 

 

 

 

 

 

 

 

 

E-22