Page 1 :
NUMERICAL METHODS, , Gauss—Legendre integration, , 1 n, [fees = Yow ses, ~ i=1, , se Wi i Wi, n=2 n=9, 0.5773502692 1.0000000000 |) 0.0000000000 0.33023 93550, 0.32425 34234 0.3123470770, n=3 0.6133714327 0.26061 06964, 0.00000 00000 0.88888 88889 || 0.83603 11073 0.18064 81607, 0.77459 66692 0.5555555556 || 0.9681602395 0.08127 43884, n=4 n= 10, 0.33998 10436 0.6521451549 |) 0.1488743390 0.29552 42247, 0.8611363116 0.34785 48451 |) 0.4333953941 0.26926 67193, 0.67940 95683 = 0.21908 63625, n=5 0.86506 33667 0.14945 13492, 0.00000 00000 0.56888 88889 || 0.9739065285 0.06667 13443, 0.5384693101 0.47862 86705, 0.9061798459 0.2369268851 |) n= 12, 0.12523 34085 0.24914 70458, n=6 0.36783 14990 =—-0.23349 25365, 0.2386191861 0.46791 39346 |) 0.5873179543 0.20316 74267, 0.6612093865 0.36076 15730 || 0.76990 26742 0.16007 83285, 0.9324695142 0.1713244924 || 0.90411 72564 0.10693 93260, 0.9815606342 0.0471753364, n=7, 0.0000000000 0.41795 91837 || n= 20, 0.4058451514 0.3818300505 |) 0.0765265211 0.15275 33871, 0.74153 11856 0.2797053915 |) 0.2277858511 0.1491729865, 0.9491079123 0.12948 49662 |) 0.3737060887 0.14209 61093, 0.51086 70020 0.13168 86384, n=8 0.63605 36807 =—-0.11819 45320, 0.18343 46425 0.36268 37834 |) 0.7463319065 0.1019301198, 0.52553 24099 0.31370 66459 |) 0.8391169718 0.0832767416, 0.79666 64774 0.22238 10345 |) 0.91223 44283 0.06267 20483, 0.96028 98565 0.10122 85363 |) 0.9639719272 0.04060 14298, 0.99312 85992 0.01761 40071, , , , Table 27.8 The integration points and weights for a number of n-point, Gauss—Legendre integration formulae. The points are given as +x; and the, contributions from both +x; and —x; must be included. However, the contribution from any point x; = 0 must be counted only once., , 1008