, =ƒ(), ≤≤ b.
, , , , . , =ƒ() ' = ƒ'() [; b], ,
1. 0 = , 1..., n = b (0 < x1 <...< n) [; b] n (. . 183). 0 = , M1,...,Mn = . 0M1, M1M2,..., n-1n, ΔL1, AL2,..., ΔLn. M0M1M2... Mn-ιMn, Ln=ΔL1 + ΔL2+...+ ΔLn =
2. ( ) ΔL1 Δxi Δi:
Δi=ƒ'(i)Δi, ci (xi-1;xi).
M0M1... n
3. l , ,
.
, ΔLi→0 Δxi →0 ΔLi = , , |Δxi|<ΔLi).
[; b], , , ƒ'(). , (41.4), max Δxi→ 0:
, l =
V , S , , : S = S(x), ≤ ≤ b.
1. [a;b] ∏, (. . 188). S(x) ; S(x) . v(x) , . , [; ] v , . . v = v(x) (v(a) = 0, v(b) = V).
2. dV v = v(x). , , +Δ, S(x) dx. dV = S(x) dx.
3. V dA :
.
, = ƒ() 0, ≤ x ≤ b = = b (. . 190). . , , ( [; b]), = ƒ(). , S(x)=πy2.
|
|
(41.6) ,
=φ() ≥ 0 = 0, = ,
= d ( < d), , , (41.7),