3, 4
--
2012 .
517.5 (08)
. . - --: , 2012.- 32 c.
3, 4. . .
, .
: ..
..
: ..
..
2012 ., .
020818 6084/16
. . . . . 2,0. 50 .
-
344022, /, . , 162
ã
, 2012
3
: F(x), F¢(x) ( F¢(x) f(x)). : f(x) F(x), f(x). F(x) ,
f(x) - . , F¢(x) = f(x), [F¢(x) + C]¢ = f(x).
- .
:
F(x) + C, f(x), ..
= F(x) + C, [F(x) + C]¢ = f(x).
f(x)dx , .. d[F(x) + C] = f(x)dx.
, .
:
f(x) = . = 1/2x2 + C.
:
.
, , :
1. | 9. |
2. | 10. |
2¢. | 11. |
3. | 12. |
3¢. | 13. |
4. | 14. |
5. | 15. |
6. | 16. |
7. | 17. |
8. | 18. |
1. , .. d ò, , . .
2. , .. .
3. , .. .
:
1
.
=
, x , t. , = j(t),
|
|
. . t : t = j(x), dt = j¢(x)dx. , j¢(x)dx.
:
, Cosx dx Sinx = t, Cosx dx = dt.
( Sinx)
2
.
=
3
.
.
4
.
=
,
2 + + :
.
:
, f(x)dx U*dV, U(x) V(x) - .
.
5
.
=
6
.
=
7
.