Some companions of perturbed Ostrowski-type inequalities based on the quadratic kernel function with three sections and applications

Journal of Inequalities and Applications

Table 1 Numerical results

f(x)	n	[a,b]	$\int_{a}^{b} f (x) d x$	$T_{n}$	Error of $T_{n}$	$Q_{n}^{1}$ and $Q_{n}^{2}$	Error of $Q_{n}^{1}$ and $Q_{n}^{2}$
cosx − x	20	$[0, \frac{π}{2}]$	−0.233701	−0.234215	5.14E-4	−0.233636	6.5E-5
$e^{2 x} cos (e^{x})$	20	[0,1]	−1.176887	−1.181466	4.579E-3	−1.176316	5.71E-4
$\frac{1}{x^{4} + 4 x^{2} + 3}$	10	[0,1]	0.241549	0.241393	1.56E-4	0.241569	2E-5
tanx + x	20	$[0, \frac{π}{4}]$	0.654999	0.655127	1.28E-4	0.654983	7E-6
$ln (x^{2} + 1)$	20	[−1,1]	0.527887	0.529554	1.667E-3	0.527679	2.08E-4