Ch20 16
- 1. Exercice 16
(a)
1
4dx b−a 1−0 1
= =
x+1 n 4 4
0
Ainsi, les différentes abscisses sont :
a=0 x1 = 1/4 x2 = 2/4 x3 = 3/4 b=1
Abscisses f (x)
0 4/(0 + 1) = 4
1/4 4/(1/4 + 1) = 16/5
2/4 4/(2/4 + 1) = 8/3
3/4 4/(3/4 + 1) = 16/7
1 4/(1 + 1) = 2
- 2. Exercice 16 (suite..)
Ce qui permet de calculer :
1
4 1 16 8 16
dx 4+2 + + +2 2, 788
x+1 8 5 3 7
0
(b)
1
4dx
= [4 · ln(x + 1)]1
0
x+1
0
= 4 · ln(2) − 4 · ln(1)
= 4 · ln(2) 2, 773