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prob_07_04_02

# prob_07_04_02 - Problem 7.4-2 Given By use of each...

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Problem 7.4-2 Given: By use of each numerical formula in Table 7.4-1, obtain four approximations for the integral of the function φ =(1+rs) -1 over a triangle. Let A=1. Solution: I A 1 1 r s + d = A 1 = J 2 A = J i 1 2 J = 1 = For a 1-point rule: r 1 1 3 := s 1 1 3 := W 1 1 := I1 1 1 r 1 s 1 + 1 1 0.9 = := For the first 3-point rule: n 3 := r 1 2 3 := s 1 1 6 := W 1 1 3 := J 1 1 := r 2 1 6 := s 2 1 6 := W 2 1 3 := J 2 1 := r 3 1 6 := s 3 2 3 := W 3 1 3 := J 3 1 := I3a 1 3 i 1 1 r i s i + J i W i = 0.924 = := For the second 3-point rule: r 1 1 2 := s 1 0 := W 1 1 3 := J 1 1 := r 2 0 := s 2 1 2 := W 2 1 3 := J 2 1 := r 3 1 2 := s 3 1 2 := W 3 1 3 := J 3 1 := I3b 1 3 i 1 1 r i s i + J i W i = 0.933 = := For the 4-point rule: r 1 1 3 := s 1
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