Quiz 2 ANDREI - Quiz 2 Problem 1 Composite Simpson's Rule...

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Quiz 2 Luarsab Imnaishvili Problem 1 Composite Simpson's Rule f(x) = x^3 ln(x) a = 13.5 b = 14.5 Accuracy 0.000010 h < 0.212132 n > 4.714045 h = 0.125000 n = 8.000000 counter node value weight term 0 13.500000 6403.592635 1 6403.592635 1 13.625000 6606.434485 4 26425.737940 2 13.750000 6813.677099 2 13627.354199 3 13.875000 7025.372624 4 28101.490497 4 14.000000 7241.573312 2 14483.146625 5 14.125000 7462.331522 4 29849.326088 6 14.250000 7687.699716 2 15375.399432 7 14.375000 7917.730461 4 31670.921844 8 14.500000 8152.476426 1 8152.476426 Approximation: 7253.726904 Actual Value: 7253.73 Error: 0.00000058
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Problem 2 Simpson Multiple Integral n = 3 m = 3 f(x) = x/y b = 14.5 d(x) = 16.5x h=(b-a)/2n a = 13.5 c(x) = 15.5x 0.166667 grid x0 x1 x2 x3 x4 x5 x 13.500000 13.666667 13.833333 14.000000 14.166667 14.333333 c(x) 209.250000 211.833333 214.416667 217.000000 219.583333 222.166667 d(x) 222.750000 225.500000 228.250000 231.000000 233.750000 236.500000 k(x) = (d-c)/2m 2.250000 2.277778 2.305556 2.333333 2.361111 2.388889 y0 209.250000 211.833333 214.416667 217.000000 219.583333 222.166667 y1 211.500000 214.111111 216.722222 219.333333 221.944444 224.555556 y2 213.750000 216.388889 219.027778 221.666667 224.305556 226.944444 y3 216.000000 218.666667 221.333333 224.000000 226.666667 229.333333 y4 218.250000 220.944444 223.638889 226.333333 229.027778 231.722222 y5 220.500000 223.222222 225.944444 228.666667 231.388889 234.111111 y6 222.750000 225.500000 228.250000 231.000000 233.750000 236.500000 weights Function Values 1.000000 0.064516 0.064516 0.064516 0.064516 0.064516 0.064516 4.000000 0.063830 0.063830 0.063830 0.063830 0.063830 0.063830 2.000000 0.063158 0.063158 0.063158 0.063158 0.063158 0.063158 4.000000 0.062500 0.062500 0.062500 0.062500 0.062500 0.062500 2.000000 0.061856 0.061856 0.061856 0.061856 0.061856 0.061856 4.000000 0.061224 0.061224 0.061224 0.061224 0.061224 0.061224 1.000000 0.060606 0.060606 0.060606 0.060606 0.060606 0.060606 Terms = weights x values 0.064516 0.064516 0.064516 0.064516 0.064516 0.064516 0.255319 0.255319 0.255319 0.255319 0.255319 0.255319 0.126316 0.126316 0.126316 0.126316 0.126316 0.126316 0.250000 0.250000 0.250000 0.250000 0.250000 0.250000 0.123711 0.123711 0.123711 0.123711 0.123711 0.123711 0.244898 0.244898 0.244898 0.244898 0.244898 0.244898 0.060606 0.060606 0.060606 0.060606 0.060606 0.060606 k(x)/3 x column 0.844025 0.854445 0.864865 0.875285 0.885705 0.896125 weights 1.000000 4.000000 2.000000 4.000000
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