f (x) [ a,b ], [ a,x ], . x
. | (7.10.1) |
F (x) . (7.10.1) t, x.
[ a,b ] f (x) . .
, [ a,b ] f (x) F (x) . F (x) , , .
7.12.
(. 7.10), [ a,b ] f (x) ,
, | (7.12.1) |
. x = a (7.12.1), (1) : C = - F (a).
(7.12.1) .
x x = b,
(7.12.2) |
(7.12.2) , .
F (b) - F (a) . (7.12.2) .
:
1) f (x) ;
2) , ;
3) .
(7.13.1) |
(7.13.1) .
, , , , , (7.13.1) . .
1. .
.t=1+ , dt = 2x dx t =1 t =2 . x =1.
.
2. .
x = a sin t.
, dx = a cos t dt, , x = 0, x = a. ,
.
: u (x) v (x) .
(7.13.2) |
(7.13.2) .
1. .
, .
.
2. .
, . (7.13.2):
.