Intégrale: méthode des rectangles
Author: Hédi Abderrahim

Animer soit en manuant l'un  au moins de des curseurs n ou i  soit en cliquant sur le bouton  ON/OFF  situé au coin bas gauche.

val de i

val de r_i

somme

val de R_i

l'intégrale[f,1,2]

                Illustration graphique 
de la valeur approchée d'une intégrale
             Méthode des rectangles

H. Abderrahim

g(x) = 1 / x
f = Function(g, 0, 1000)
n = 9 (slider from 1 to 10, step 1)
S_n = UpperSum(f, 1, 2, n)
s_n = LowerSum(f, 1, 2, n)
i = 7 (slider from 1 to 10, step 1)
r_i: 1 / n * f(1 + i / n)
R_i: 1 / n * f(1 + (i - 1) / n)
A2 = 1
A3: A2 + 1
A4: A3 + 1
A5: A4 + 1
A6: A5 + 1
1 / 5 * 1 / ((A2 - 1) / 5): 1 / (A2 - 1 + 5)
B2: 1 / n * 1 / (1 + A2 / n)
B3: 1 / n / (1 + A3 / n)
B4: 1 / n / (1 + A4 / n)
B5: 1 / n / (1 + A5 / n)
B6: 1 / n / (1 + A6 / n)
A7: A6 + 1
A8: A7 + 1
A9: A8 + 1
A10: A9 + 1
A11: A10 + 1
B7: 1 / n / (1 + A7 / n)
B8: 1 / n / (1 + A8 / n)
B9: 1 / n / (1 + A9 / n)
B10: 1 / n / (1 + A10 / n)
B11: 1 / n / (1 + A11 / n)
B28 = Sum(B2:B11)
D2: 1 / n * n / (n + A2 - 1)
D3: 1 / n * n / (n + A3 - 1)
D4: 1 / n * n / (n + A4 - 1)
D5: 1 / n * n / (n + A5 - 1)
D6: 1 / n * n / (n + A6 - 1)
D7: 1 / n * n / (n + A7 - 1)
D8: 1 / n * n / (n + A8 - 1)
D9: 1 / n * n / (n + A9 - 1)
D10: 1 / n * n / (n + A10 - 1)
D11: 1 / n * n / (n + A11 - 1)
D28 = Sum(D2:D11)
C2 = Integral(f, 1, 2)
C3 = Integral(f, 1, 2)
C4 = Integral(f, 1, 2)
C5 = Integral(f, 1, 2)
C6 = Integral(f, 1, 2)
C7 = Integral(f, 1, 2)
C8 = Integral(f, 1, 2)
C9 = Integral(f, 1, 2)
C10 = Integral(f, 1, 2)
C11 = Integral(f, 1, 2)
C28: C11
B = (0.6189491399075523, 0.43856039299175975)
C = (0.3924842612043238, 0.8704236500537305)
texte1: "s_n =" + s_n
texte2: "S_n = " + S_n
I = Integral(f, 1, 2)
texte3: " \int_{1 }^{ 2} f(x).dx = " + I