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deff(’y=f(x)’,’y=sqrt(1 + x^2)’) //G-L n=2 x2 = sqrt(3)/3 w2 = 1 I2 = w2(1)*f(x2(1)) + w2(1)*f(-x2(1)) disp(I2) //G-L n=3 x3 = [0 -sqrt(3/5) sqrt(3/5)] w3 = [8/9 5/9 5/9] I3 = w3(1)*f(x3(1)) + w3(2)*f(x3(2)) + w3(2)*f(-x3(2)) disp(I3) //G-L n=4 x4 = [sqrt((3-2*sqrt(6/5))/7) sqrt((3+2*sqrt(6/5))/7)] w4 = [(18+sqrt(30))/36 (18-sqrt(30))/36] I4 = w4(1)*f(x4(1)) + w4(1)*f(-x4(1)) . + w4(2)*f(x4(2)) + w4(2)*f(-x4(2)) disp(I4) //G-L n=5 x5 = [0 1/3*sqrt(5-2*sqrt(10/7)) 1/3*sqrt(5+2*sqrt(10/7))] w5 = [128/225 (322+13*sqrt(70))/900 (322-13*sqrt(70))/900] I5 = w5(1)*f(x5(1)) + w5(2)*f(x5(2)) + w5(2)*f(-x5(2)) . + w5(3)*f(x5(3)) + w5(3)*f(-x5(3)) disp(I5) Os coeficientes da quadratura de Gauss-Legendre foram obtidos no intervalo [ − 1 , 1 ] . Para aproximar a integral de f ( x ) no intervalo [ a , b ] devemos fazer a mudança de variável x ̄ i = α t i + β , α = ( b − a ) ∕ 2 , β = ( b + a ) ∕ 2 (9.206) Quando subdividimos o intervalo inicial [ a , b ] em N intervalos com extremos [ x i , x i + 1 ] a transformação torna-se x ̄ i = α t i + β , α = ( x i + 1 − x i ) ∕ 2 , β = ( x i + 1 + x i ) ∕ 2 (9.208) Exemplo 9.7.2. Aproximar I = ∫ 0 1 1 + x 2 d x (9.210) Solu ç ã o. Para tanto, fazemos a mudança de variáveis u = 2 x − 1 : I = ∫ 0 1 1 + x 2 d x = 1 2 ∫ − 1 1 1 + u + 1 2 2 d u . PSG x Montpellier: onde app de aposta probabilidade de futebol assistir ao jogo pelo Campeonato Francês. Aproxime a integral de sen ( x ) em [ 0 , 1 ] utilizando 5 intervalos iguais e em cada intervalo utilize uma quadratura gaussiana com 3 nós. Loteria c.
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