A Note on Finite Quadrature Rules with a Kind of Freud Weight Function

Table 3

∫^+∞_−∞𝑥⁻¹⁰e(−1/𝑥²)𝑓(𝑥)𝑑𝑥.

𝑓(𝑥)	Approx. value (4-point)	Exact value	Error
√1+cos𝑥^2	16.21776936	16.21978539	0.002016030
(1+𝑥^2)^−1/2	10.30987753	10.31704740	0.007116987
exp(−𝑥^2−2)	1.198219038	1.199125136	0.000906098