Midpoint Derivative-Based Closed Newton-Cotes Quadrature

Table 2

Computational cost to estimate ∫¹₀(𝑑𝑥/(1+𝑥)).

Formula	Order	Subintervals	Func. eval	Mid. deriv	Total
Trapezoidal rule	2	25001	25002	0	25002
Simpson’s rule	4	67	135	0	135
Simpson’s 3/8 rule	4	55	166	0	166
Bool’s rule	6	10	41	0	41
Mid. deriv. Trapezoidal rule	4	105	106	105	211
Mid. deriv. Simpson’s rule	6	14	29	14	43
Mid. deriv. Simpson’s 3/8 rule	6	12	37	12	49
Mid. deriv. Bool’s rule	8	5	21	5	26