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

Table 13

Rules	Integral
	Approximate value of 𝑇1=∫^1−1𝑒^𝑥𝑑𝑥	Absolute error
𝑅1(𝑓)	2.3503966	5.8×10^−6
𝑅2(𝑓)	2.3504046	2.2×10^−6
𝑅3(𝑓)	2.3504034	1.0×10^−8
Exact value	2.3504024Correct to seven decimal places	**