F (x), f (x), ..
F ¢(x) = f (x) (4.1)
f (x). , , , ,
, .
f (x) = sin (2 x), F (x) = - 0.5 cos(2 x),
.
. F 1(x) F 2(x) f (x) [ a, b ]. .
. () F 2(x) F 1(x), .. () = F 2(x) - F 1(x) ()
(4.2)
, , , () = const ≡ C
F 2(x) = F 1(x) + . (4.3)
. f (x) { F (x)}, , .. { F (x)}= F (x) + C.
. f (x) = sin(2x) F (x) = 0.5 cos(2 x), F (x) = 0.5 cos(2 x) +4, F (x) = 0.5 cos(2 x) -1, . , F (x) = 0.5 cos(2 x) + C
{ F (x)} f (x)
, (4.4)
ò - , ,
f (x) - ,
f (x)d x - ,
C - .
,
.
()¢ = (F (x) + C)¢ = F ¢(x) + 0 = f (x). (4.5)
. , d F = F ¢(x)d x,
d () = ()¢ d x = f (x) dx. (4.6)
. , F (x) - f (x) (.. F ¢(x) = f (x)).
(4.7)
(4.5 4.7) , . .
.
.
(4.8)
|
|
.
(4.9)
(4.8) (4.9) . (4.8) , . (4.5)
, . (4.9) . . 3.
. .
. , (1 = sin2 x + cos2 x), , :
=
3.