Интегральное исчисление. Определенный интеграл - 13 стр.

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ЮФУ | Ростов-на-Дону

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n = 6
f [a, b] T
[a, b]
a = x
0
< x
1
< x
2
< . . . < x
n−1
< x
n
= b.
M
i
= sup
½
f(x) : x ∈ [x
i−1
, x
i
]
¾
, m
i
= inf
½
f(x) : x ∈ [x
i−1
, x
i
]
¾
.
S = S (T ) = S
f
(T ) =
n
X
i=1
M
i
∆x
i
s = s (T ) = s
f
(T ) =
n
X
i=1
m
i
∆x
i
f
T [a, b]
s
f
(T ) ≤ S
f
(T ) ,
m
i
≤ M
i
i
[x
i−1
, x
i
] m
i
≤ f(x) ≤ M
i
I {x
i
, ξ
i
} T

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