Tabela de Integração numérica

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1
∫ b
a
f(x)dx =
∫ 1
−1
F (t)dt ≈
N∑
i=0
AiF (ti).
Tabela 1 - Gauss-Legendre
N + 1 ti Ai
2
t0 = −0.5773502691 A0 = 1
t1 = +0.5773502691 A0 = 1
t0 = −0.7745966692 A0 = 0.5555555556
3 t1 = 0.0000000000 A1 = 0.8888888889
t2 = +0.7745966692 A2 = 0.5555555556
t0 = −0.8611363115 A0 = 0.3478548451
4
t1 = −0.3399810435 A1 = 0.6521451548
t2 = +0.3399810435 A2 = 0.6521451548
t3 = +0.8611363115 A3 = 0.3478548451
t0 = −0.9061798459 A0 = 0.2369268850
t1 = −0.5384693101 A1 = 0.4786286704
5 t2 = 0.0000000000 A2 = 0.5688888888
t3 = +0.5384693101 A3 = 0.4786286704
t4 = +0.9061798459 A4 = 0.2369268850
t0 = −0.9324695142 A0 = 0.1713244923
t1 = −0.6612093864 A1 = 0.3607615730
6
t2 = −0.2386191860 A2 = 0.4679139345
t3 = +0.2386191860 A3 = 0.4679139345
t4 = +0.6612093864 A4 = 0.3607615730
t5 = +0.9324695142 A5 = 0.1713244923
2
∫ b
a
f(x)dx =
∫ 1
−1
F (t)dt ≈
N∑
i=0
AiF (ti).
Tabela 2 - Gauss-Tchebyshev
N + 1 ti Ai
2
t0 = −0.7071067811 A0 = 1.570796326
t1 = −0.7071067811 A1 = 1.570796326
t0 = −0.8660254037 A0 = 1.047197551
3 t1 = 0.0000000000 A1 = 1.047197551
t2 = +0.8660254037 A2 = 1.047197551
t0 = −0.9238795325 A0 = 0.7853981633
4
t1 = −0.3826834323 A1 = 0.7853981633
t2 = +0.3826834323 A2 = 0.7853981633
t3 = +0.9238795325 A3 = 0.7853981633
t0 = −0.9510565162 A0 = 0.6283185307
t1 = −0.5877852522 A1 = 0.6283185307
5 t2 = 0.0000000000 A2 = 0.6283185307
t3 = +0.5877852522 A3 = 0.6283185307
t4 = +0.9510565162 A4 = 0.6283185307
t0 = −0.9659258262 A0 = 0.5235987755
t1 = −0.7071067811 A1 = 0.5235987755
6
t2 = −0.2588190451 A2 = 0.5235987755
t3 = +0.2588190451 A3 = 0.5235987755
t4 = +0.7071067811 A4 = 0.5235987755
t5 = +0.9659258262 A5 = 0.5235987755
3
∫ ∞
a
f(x)dx =
∫ ∞
0
F (t)dt ≈
N∑
i=0
AiF (ti).
Tabela 3 - Gauss-Laguerre
N + 1 ti Ai
2
t0 = 0.5857864376 A0 = 0.8535533905
t1 = 3.4142135620 A1 = 0.1464466094
t0 = 0.4157745567 A0 = 0.7110930099
3 t1 = 2.2942803600 A1 = 0.2785177335
t2 = 6.2899450820 A2 = 0.0103892565
t0 = 0.3225476896 A0 = 0.6031541043
4
t1 = 1.7457611010 A1 = 0.3574186924
t2 = 4.5366202960 A2 = 0.0388879085
t3 = 9.3950709120 A3 = 0.5392947055× 10−3
t0 = 0.2635603197 A0 = 0.5217556105
t1 = 1.4134030590 A1 = 0.3986668110
5 t2 = 3.5964257710 A2 = 0.0759424497
t3 = 7.0858100050 A3 = 0.3611758679× 10−2
t4 = 12.640800840 A4 = 0.2336997238× 10−4
t0 = 0.2228466041 A0 = 0.4589646739
t1 = 1.1889321010 A1 = 0.4170008307
t2 = 2.9927363260 A2 = 0.1133733820
t3 = 5.7751435690 A3 = 0.0103991975
t4 = 9.8374674180 A4 = 0.2610172028× 10−3
t5 = 0.1598297398× 102 A5 = 0.8985479064× 10−6
4
∫ ∞
−∞
f(x)dx =
∫ ∞
−∞
F (t)dt ≈
N∑
i=0
AiF (ti).
Tabela 4 - Gauss-Hermite
N + 1 ti Ai
2
t0 = −0.7071067811 A0 = 0.8862269254
t1 = +0.7071067811 A1 = 0.8862269254
t0 = −1.2247448710 A0 = 0.2954089751
3 t1 = 0.0000000000 A1 = 1.1816359000
t2 = −1.2247448710 A2 = 0.2954089751
t0 = −1.6506801230 A0 = 0.0813128354
4
t1 = −0.5246476323 A1 = 0.8049140900
t2 = +0.5246476323 A2 = 0.8049140900
t3 = +1.6506801230 A3 = 0.0813128354
t0 = −2.0201828700 A0 = 0.0199532421
t1 = −0.9585724646 A1 = 0.3936193231
5 t2 = 0.0000000000 A2 = 0.6453087204
t3 = +0.9585724646 A3 = 0.3936193231
t4 = +2.0201828700 A4 = 0.0199532421
t0 = −2.3506049730 A0 = 0.4530009905× 10−2
t1 = −1.3358490740 A1 = 0.1570673203
6
t2 = −0.4360774119 A2 = 0.7246295952
t3 = +0.4360774119 A3 = 0.7246295952
t4 = +1.3358490740 A4 = 0.1570673203
t5 = −2.3506049730 A5 = 0.4530009905× 10−2