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

Table 4

Rules	Integral
	Approximate value of 𝐼4=𝑃∫^3(1+𝑖)/2(1+𝑖)/2(sin𝑧/(𝑧−(1+𝑖)))𝑑𝑧	Absolute error
𝑅1(𝑓)	1.8175586−0.2057251∗𝑖	1×10^−7
𝑅2(𝑓)	1.8175587−0.2057251∗𝑖	0.0
𝑅3(𝑓)	1.8175587−0.2057251∗𝑖	0.0
Exact value	1.8175587−0.2057251∗𝑖	**