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

Table 10

Rules	Integral
	Approximate value of 𝑄2=𝑃∫^1/4−1/4((𝑥+1)/𝑥(𝑥^2+1))𝑑𝑥	Absolute error
𝑅1(𝑓)	0.4899564	9.0×10^−7
𝑅2(𝑓)	0.4899576	3.0×10^−7
𝑅3(𝑓)	0.4899574	1.0×10^−7
Exact value	0.4899573	**