-
2012
: - / - ; . .. , .. . , 2012. 22 .
. , , , . - , .
- , 2012
.
1. 녅................ 3
2. .. 5
4. ⅅ.. 8
5. 10
5.1 充10
5.2 酅. 11
5.3 셅. 12
6. 14
7. 1.. 17
8. 20
9. ꅅ 22
1.
. f(x). F(x),
F'(x) = f(x) (1)
: f(x) = 65. F(x). : F(x) = 6 + , - const 1: F(x) f(x), (1).
:
) f(x);
) .
1. f(x) [, ], F(x) [, ] ( )
2. F(x) - f(x), F(x) + , - , f().
:
[ F(x) + ]' = F' () + ', . . '=0, F' (x) =f(x),
.
, f(x) , . , f(x) = 65 6, 6 + 3, 6 + 1 ..
3. f(x) F(x), F(x) + .
: . f(x) 2 F(x) (). (1)
F' (x) =f(x) ' () =f(x).
|
|
F' () - ' () = 0 [F () - ()]' = 0. F ()- () = , - .
() = F () + ,
.
, f(x)= 5 6 6 + .
2. f(x)
∫f(x)dx = F(x) +
f () - , f ()dx - , - - . ,
3. .
2.
∫xdx = + - f(x) = .
:
= 0
= 1
= -2
, ∫f(x)dx = F(x) + ,
OY. . : = 0, . ,
[F(x) + ]' = F'(x) │ = f(x0).
3.
1.
(3)
.
,
.
2.
(4)
.
,
.
3.
(5)
. (5)
, , (5) .
4.
(6)
. (6).
(∫ f(x)dx)'= a f(x)
(a ∫ f(x)dx)' = a(∫ f(x)dx)' = a f(x)
, , (6) .
5. .
(7)
.
,
f1 ()+f2(), , . . , (7) (7) .
6.
. ∫f(x)dx = F(x) + = φ () - , .
∫f(u)du = F(u) + (8)
. F'(x) =f(x).
F(u) =F(φ(x)). 1-
dF(u) = F'() du = f(u)du
∫dF(u) = F'(u)du = ∫f(u)du = F(u) + ,
.
:
4.
. .
|
|
1. 8.
2. 9.
3. 10.
4. 11.
5.
12.
7. 13.
, , 8
,
.
11:
: , .
:
- ,
-
- ,
- ,
-
.
:
5.
, .
.
:
1.
:
2.
:
3.
:
4.
: