Midpoint Derivative-Based Closed Newton-Cotes Quadrature

Table 7

Int.	Simpson’s rule		Midpoint derivative Simpson’s rule
	Approximate value	Error	Approximate value	Error
1	3.1333333333	0.0082593203	3.1463040000	0.0047113464
2	3.1415686275	0.0000240261	3.1416054730	0.0000128194
4	3.1415925024	0.0000001512	3.1415927140	0.0000000604