ABSTRACT
Table 6.8 presents t; and C; for n = 2, 3, and 4. Higher-order results are presented by Abramowitz and Stegun (1964).
Example 6.6. Gaussian quadrature
To illustrate Gaussian quadrature, let's solve the example problem presented in Section 6.1, wheref(x) = I/x, a = 3.1, and b = 3.9. Consider the two-point formula applied to the total range of integration as a single interval. From Eq. (6.73),
b+a c=--=352 . (6.79)
Equations (6.74) and (6.76) become
x = OAt + 3.5 and F(t) IOAt + 3.5
(6.80)
Substituting these results into Eq. (6.78) with n = 2 gives
1= 004 fl F(t) dt = OA[(l)F(~) + (l)F(~)] (6.81 )
