ABSTRACT
The error is Error = 0.22957443 - 0.22957444 = -0.00000001. This result is comparable to Simpson's 1/3 rule with h = O. I.
As a final example, let's evaluate the integral using the sixth-order formula based on the fifth-degree Newton forward-difference polynomial. That formula is (see Table 604)
5h 1 = 288 (19/0 + 75/i + 50h + 50./3 + 7514 + I9fs) + O(h7)
For five equally spaced increments, h = (3.9 - 3.1)/5 = 0.16. Thus,
1 = 5~~~6) [19(1/3. I0) + 75( I/3.26) + 50(1/3042) + 50(1/3.58) + 75(1/3.74) + 19(1/3.90)]
= 0.22957445
(6.95)
(6.96) The error is Error = 0.22957445 - 0.22957444 = 0.00000001. This result is comparable to Gaussian quadrature with three points.
