f (x) = , , = (n 1, , nk).
. = =
= = = + + =
= + + = +
+ + .
[ a, b ] = f (x). = b. [ i 1; xi ] (i = 1, 2,, ) , . f (x) [ a, b ], , , = f (x) b :
.
= f (x) [ a, b ].
:
t , f (t) t.
:
1. .
2. = + .
3. .
-
= f (x) [ a, b ] F (x) f (x), -
.
= (), v = v (x) [ a, b ],
.
, [ ], , ,
.
, (. 18) = f 1(x), =
= f 2(x) (f 1(x) f 2(x)) = , = b,
.
. 18 |
1. y = f (x)?
2. y = f (x)?
3. ?
4. ?
5. ? ?
6. ?
7. ?
8. ?
9. ?
10. ?
11. ?
2
:
1) ;
2) ;
3) .
.
. 1) , , u = x 4,
.
= = = =
= .
: = = = =
= .
2) :
u = arctg 2 x du = , dv = xdx v = .
=
= =
= =
.
: =
+ + ' = + +
+ + 0 = + + = = + + = + =
= .
3) , , :
|
|
x 2 3 x + 2 | |||
2 x + 6 | |||
14 x 13 | |||
, .
= dx + dx = [ 2 3 + 2 =
= ( 1) ( 2)] = + = I.
:
= = = .
,
14 13 = ( + ) + (2 ).
,
= .
, = +15 =
= + = + + .
: = ( 2) ' + (6 ) '
(ln | x 1|) ' + (15 ln| x 2|) ' + c' = 2 x + 6 (x 1) ' +
+ (x 2) ' + 0 = 2 x + 6 + =
= =
= =
= = .
: 1) ; 2) ;
3) + + .
3
, y = x 2 7 x +
+ 12, y = x 3.
. , . 19.
. 19 |
. :
= 3, = 5. , = 3, b = 5.
, = =
= = = (. .).
: . .
3. 4 5