Chapitre 3 : Intégration

F f I
F′(x) = f(x)x I.
F(x)f(x)k F (x) + k
f
f F (x) + k
a b f
b
a
f(x)dx =F(b)−F(a) = f

q
CT(q)q
CM(q) = CT(q)
q
q
Cm(q) = C′
T(q)q
CT(0) =
X f X
a b
(a < X < b) = b
a
f(x)dx
N(0,1) −x2/2
√2π
a
f(x) = a−ax x≥0
0x < 0
E(X) = 1
aV(X) = 1 a
f(x) = 1 g(x) = 6x2h(x) = 6
x2k(x) = 2 x
j(x) = 3x+1 l(x) = 4
(x+ 3)3p(x) = x3+x2
F f F (0) = 4
G g G(1) = 0

K k K(1) = 2
f(x) = 2xx2g(x) = x2
x3+1 h(x) =
x
x+ 1
I=0
−2
3dx J =−2
0
3dx K =2
1
−4t dt H =4
0
(3s2+ 1) ds
f F
F(x) = x
3
f(t)dt
F
F(3)
F(x)f(x) = 2x f(x) = x.
f
y
3
2
1
0
-1 x
-2
-3
3210-1-2-3
F(x) = x
−2
f(t)dt ?
4
3
x
2
3
-2
-1 20-2
1
01-1-3
y
3
2
1
0
-1 x
-2
-3
3210-1-2-3

2
1x
03
-4
-3
20-2
-1
-2
1-1-3
6
5
x
4
3
0
1
20-2
3
2
1-1-3
G f
x0G(x) = x
x0f(t)dt
Cm(q) = 3q2−30q+ 100
CT(q)
CM(q)
q0
CM(q0) = Cm(q0)
q0
CM(q0) = Cm(q0)
T