f(x) .
. F(x) f(x) , F(x) , F'(x) = f(x).
. F1(x) F2(x) f(x) , F1(x) - F2(x)= onst =C. .
:
F1(x) F2(x) f(x) F1(x) - F2(x)= f(x) .
F1(x) - F2(x)=λ(x).
λ(x) = F1(x) - F2(x) = f(x)- f(x)=0 ( ).
, λ(x)= onst =C F1(x) - F2(x) = C.
. F(x)- f(x) , - (x) (x)=F(x)+C, .
. f(x) f(x) , - , - , - , - .
: = F(x)+, F(x) , - .
1. ,
= , F(x) = , F'(x)= (
1.
, .
$ , (1) = F(x)+ (α), F'(x) = f(x) (β).
.
2.
.
3. ˳
,
[ = =
4. ˳ = c , (c - const)
. 3.
( |
1. (1),
(1) F(t) = f(t), (2) [ ]= F() = f()
1.
.
.
2.
[ ] =
. { + C.
:
. , , .
, :
: ; : , , , , .
. u(x) i v(x) . v(x)* u(x) ( $ (1)
. . : [ ] = + (2)
$ , 1 = $ . (2) (1) ( , ).
.
. :
1) t=φ(x) , φ(x).
|
|
2) g(t) G(t) T ( $ , . (1).
. .
(1) [ ]= G(.
. t= , f(x)dx = . .
, , . = =
. =
,
. =