.


:




:

































 

 

 

 





. . . .

F(x) f(x), , F(x) , : F(x) = f(x)

1. F(x) F(x), F(x)+C . , (x) y = f(x) (x) = F(x)+C, F(x) - , C - .

:

F(x) = f(x). , ,

(F(x)+C) = F(x)+C = F(x) = f(x). , F(x)+C y = f(x). , y = f(x) F(x) - , (x)

(x) = F(x)+C

,

Ԓ(x) = F(x)+C F(x) = f(x).

, , . , (x) = F(x)+C, .

.

y = f(x) ∫f(x)dx = F(x)+C

f(x) , f(x)*dx - .

: " " " ", : ,

1. (f(x)dx) = f(x)

2. ∫f′(x)dx = f(x) + c

3. ∫a ⋅ f(x)dx = a∫f(x)dx, a ≠ 0

4. ∫(f1(x) + f2(x))dx = ∫f1(x)dx + ∫f2(x)dx

 

.

(. . ). , ( ). .

pyc ∫f(x)dx. =φ(t), φ(t) - , . dx=φ'(t) dt peeoo poa caoo ∫f(x)dx = ∫f(φ(t)) * φ(t)dt eo . oe t .

u=u() ν=v() - , . d(uv)=udv+vdu.

, ∫d(uv) = ∫udv + ∫vdu

∫udv =uv - ∫vdu

. ∫udv ∫vdu, , .

, - pao dv (, , c); , ν du, . .

 





:


: 2016-10-30; !; : 1200 |


:

:

, , .
==> ...

1102 - | 863 -


© 2015-2024 lektsii.org - -

: 0.013 .