Интегральное исчисление. Определенный интеграл - 31 стр.

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c
[a, b]
c ∈ (a, b) f ∈ R [a, c] f ∈ R [c, b]
f [a, c] [c, b]
[a, b] m M
m ≤ f(x) ≤ M, x ∈ [a, b] .
M = m f(x) = C = const f ∈ R [a, b]
b
Z
a
f(x) dx = C (b −a) ,
c
Z
a
f(x) dx = C (c − a) ,
b
Z
c
f(x) dx = C (b − c) .
C (b − a) = C (c − a)+ C (b − c)
M > m ε > 0
f [a, c] [c, b]
δ T
0
T
00
[a, c]
[c, b] δ
X
0
ω
i
∆x
i
<
ε
4
,
X
00
ω
i
∆x
i
<
ε
4
,
T
0
[a, c]
T
00
[c, b]
δ <
ε
2 (M − m)
.
T
δ a = x
0
< x
1
< x
2
< . . . < x
n−1
< x
n
= b
T
x = c T T
T
0
[a, c] T
00
[c, b]
δ
n
X
i=1
ω
i
∆x
i
=
X
0
ω
i
∆x
i
+
X
00
ω
i
∆x
i
,

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