New Derivative Based Open Newton-Cotes Quadrature Rules

Table 1

Coefficients of error term for each order of accuracy.

Order	𝑁0	ONC	𝑁0	ONC1	𝑁0	ONC2	𝑁0	ONC3	𝑁0	ONC4
4	3	1445≈0.31	2	780≈0.08	1	7180≈0.04	2	780≈0.08	1	7180≈0.04
6	5	41140≈0.29	3	1074725≈0.02	2	316720≈0.005	3	1074725≈0.02	3	1244725≈0.03
8	7	395614175≈0.28	4	59511016064≈0.01	3	16012182950≈0.001	5	77339200≈0.02	5	283411538600≈0.02