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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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