28

  1. Amp; 37. ³ '.
  2. II. ³
  3. IV. ²²Ͳ ²
  4. V. ²²Ͳ ̲
  5. . . . ?
  6. . . .

.

: , v(t). s(t). s(t), v(t), , . y=f(t) X.

: F(x) f(x) X, " xIX: F'(x) = f(x).

.

s(t) - v(t).

F(x) = Ln x- f(x) = (0, + ?). F(x) = Ln (-x) - f(x) = (- ?, 0).

F(x) = Ln?x?- f(x) = (- ?, 0) (0, + ?).

f(x) = ?x? = .

F(x) = .

, F'(0) 0.

f(x) = Sgn x = .

F(x) = x- f(x) = Sgn x x> 0.

F(x) = -x- f(x) = Sgn x x<0.

()

f(x) = Sgn x .

// . ³, F(x) - f(x) X, " xIX: F'(x) = f(x), F(x) +C (C= Const) - f(X) X, " xIX: (F(x) +C) '=F'(x) +C'=f(x).

³ :

5.1( ). F1(x) F2(x) - - f(x) X, F1(x) -F2(x) = Const X.

.

: F(x) = F1(x) -F2(x). , F(x) = Const X.

" xIX: F '(x) = - = 0.

, : F '(x) = 0 " xIX, F(x) = Const X. , .

. F(x) - f(x) X, - F(x) : F(x) = F(x) +C, C- .

: f(x) X X . f(x) . f(x)dx . ³, f(x). :

dF(x) =F '(x)dx= f(x)dx.(1)

5.1 :

= F(x) +C, (2)

F(x) - f(x), C- .

.

= sinx + C.

: ? ϳ , - X f(x) .

.

= f(x)dx.

= F(x) +C.

1 2 (1) (2) 1.

= .

.

F(x) - f(x), G(x) - g(x). F'(x) = f(x), G '(x) = g(x), = F(x) +C1, = G(x) +C2. , :

= [F(x) G(x)] + (12). (1)

, [F(x) G(x)] '=F '(x) G '(x) = f(x) g(x).

= [F(x) G(x)] +. (2)

, , .

=> = .

k- , =k .

.

.

1. = +C(A?-1).

2. = ln?x? +C (x?0).

3. = sinx + C.

4. = cosx + C.



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