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Numerical integration - Examples

Examples [4]

Let's consider integral of probability:

Exact value of integral of probability up to the fifth digit is equal to 2.3925.

E x a m p l e  1.  Calculate integral of probability from the trapezoid formula with step h = 1.0, 0.5, 0.25.

S o l u t i o n .   Results of calculations are tabulated:

Step of integration

h

Value of

integral

Received error:

Absolute Relative, %

1.0

2.3484

– 0.0441                1.843

0.5

2.3813

– 0.0112                0.468

0.25

2.3898

– 0.0027                0.113

E x a m p l e  2.  Calculate integral of probability by Simpson’s rule with step h = 1.0, 0.5, 0.25.

S o l u t i o n .   Results of calculations are tabulated:

Step of integration

h

Value of

integral

Received error:

Absolute Relative, %

1.0

2.3743

– 0.0182             0.760

0.5

2.3923

– 0.0002             0.008

0.25

2.3926

+ 0.0001             0.004

The given examples show, how much Simpson's rule is more exact than the trapezoid formula.


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