Midpoint Derivative-Based Closed Newton-Cotes Quadrature

Table 8

Int.	Simpson’s 3/8 rule		Midpoint derivative Simpson’s 3/8 rule
	Approximate value	Error	Approximate value	Error
1	3.1384615385	0.0031311151	3.1442262792	0.0026336256
2	3.1415834498	0.0000092038	3.1415998256	0.0000071720
4	3.1415925939	0.0000000596	3.1415926879	0.0000000343