Some Derivative-Free Quadrature Rules for Numerical Approximations of Cauchy Principal Value of Integrals

Table 17

Rules	Integral
	Approximate value of 𝑇5=∫^10(1/(1+𝑒^𝑥))𝑑𝑥	Absolute error
𝑅1(𝑓)	0.37988552	3.0×10^−8
𝑅2(𝑓)	0.37988548	1.0×10^−8
𝑅3(𝑓)	0.37988549	0.0
Exact value	0.37988549	**