On Corrected Quadrature Rules and Optimal Error Bounds

Table 6

Results for the first Simpson rule.

First Simpson rule
	Standard rule ()
	Computed	Absolute error	Relative error	Estimated order
	integral	ABS()	REL()
5	1.4464710917857768	0.0000297595376417
10	1.4464431687701778	0.0000018365220427		4.0
15	1.4464416936771560	0.0000003614290209		4.0
20	1.4464414464499289	0.0000001142017938		4.0
25	1.4464413789949659	0.0000000467468309		4.0
	Corrected rule ()
	Computed	Absolute error	Relative error	Estimated order
	integral	ABS()	REL()
5	1.4464414152480176	0.0000000829998825
10	1.4464413342388578	0.0000000019907227		5.4
15	1.4464413324310201	0.0000000001828850		5.9
20	1.4464413322811487	0.0000000000330136		6.0
25	1.4464413322568439	0.0000000000087088		6.0