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

Table 2

∫^+∞_−∞𝑥⁻⁸exp(−1/𝑥²)𝑓(𝑥)𝑑𝑥.

𝑓(𝑥)	Approx. value (3-point)	Exact value	Error
exp(−cos𝑥)	1.494420894	1.492841821	0.001579073
√1+sin𝑥^2	3.866024228	3.866700560	0.000676332
√1+cos𝑥^2	4.544708979	4.561266761	0.016557782