(a) L (d) 'J cosds COS S sp. ds (b) (e) L s² ds (c) sds "J s³ ds (J) L L scoss ds (g) -st)'] (45 - - 2s)ds 1 Table 10-1 Table for Newton-Cotes intervals and points for integration, n y(x) dx = hΣ Civi i=0 Intervals, No. of i Points, n Co C₁ C₂ C3 C4 C5 C6 234567 123456 1/2 1/2 (trapezoid rule) 1/6 4/6 1/6 (Simpson s 1/3 rule) 1/8 3/8 3/8 1/8 (Simpson s 3/8 rule) 7/90 32/90 12/90 32/90 7/90 19/288 75/288 41/840 216/840 50/288 50/288 75/288 19/288 27/840 272/840 27/840 216/840 41/840 Table 10-2 Table for Gauss points for integration from minus one to one, n L', y(x) dx dx = Σ i=1 Wiyi Number of Points 1 Associated Locations, Xi Weights, Wi 2.000 = = X₁ = 0.000... X1 +0.57735026918962 +0.77459666924148 X1, X4 = x2 = 0.000... +0.8611363116 23 2 X1, X2 3 X1, X3 4 X2, X3 = +0.3399810436 510 = 1.000 0.555... = 0.888... 0.3478548451 0.6521451549