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4-5
Numeric integrations
d
Numeric integration is a method of obtaining
the approximate solution of f
Example:
:
f(x)dx for a given function. (See figure below.)
Obtain the area of the shaded portion shown
in the
h
Divide interval (a; b).into n equal parts (n to be
an even number) and obtain the
shall be 0.0001
graph below, Relative error
area by approximating the curve of
each minimal interval with a parabola.
:
(Simpson's rule)
y
f(x)
-
f(x) =LNz
;
|
|
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x
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nS
a
b
i
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This computer automatically sets the namber
of divisions and outputs the results
'
when the relative error between the value
Sp, when divided into n parts, and the
|
value Sy_2, when divided into n-2 parts,
is within the relative error range.
:
Displays results when relative error Err >
[Sq - Sp-gl. Even if nis 146, impossi-
|
Operation:
ble will be displayed indicating calculation
was not possible if the above expres-
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sion is not satisfied.
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.
.
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(E) (Selects relative error input.)
© Numeric Integration Menu
|
ATE@Eme
(Relative exor
Numeric integration can be started by
selecting Sim (pressing key (8) ) from
the
i
TF) elects functi
input)
:
s
fun
i
software menu, The numeric
integration menu will be displayed
as shown below.
|
a
w ° i input.)
i
xe}
(Inputs function f (x).)
|
TesfS)e@e
Cnputs interval.)
#
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1.2958
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Here, § = 1,2958 is obtained.
The following processes can be selected
from this numeric integration menu.
(.....
(F(X)
Input and calculation of function and interval
a, b.
|
S)..... (8)
Confirmation of area
'
(E)..... (En)
Input of-relative error range
|
:
76
77
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