Simpson s three-eighths rule

Another rule, Simpson s three-eighths rule, is given by... 

In cases where n is divisible neither by 2 nor by 3, the range of integration may be split into two parts, one for Simpson s one-third rule, the other for Simpson s three-eighths rule. Alternatively, if the curve is approximately linear in one or two intervals, the trapezoidal rule may be used in these intervals. 

Simpson s three-eighths rule (four-point) (Figure A-4). An improved version of Simpson s one-third rule can be made by applying Simpson s second rule ... 

Examples.—(1) Compare Simpson s one-third rule and the three-eighths rule when h = 1, with the result of the integration of... 

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