Casio fx-115ES PLUS - Manual (Page 23)

E-22
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
–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.
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
S Positive
S Negative
∫ ∫ ∫
a
b
f(x)dx =
a
c
f(x)dx + (–
c
b
f(x)dx)
Positive Part
( S Positive)
Negative Part
( S Negative)
∫ ∫ ∫
a
b
f(x)dx =
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)
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 +
x
1
x
2
f(x)dx + .....
∫ ∫ ∫
x
4
b
f(x)dx
∫
+
a
b
f(x)dx =
a
x
1
f(x)dx +
x
1
x
2
f(x)dx + .....
∫ ∫ ∫
x
4
b
f(x)dx
∫
+