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Mathematics
Mathematics
Problem
Let
f
f
f
be a continuous function on
[
a
,
b
]
[a, b]
[
a
,
b
]
. Prove that there exists a number
x
∈
[
a
,
b
]
x \in [a, b]
x
∈
[
a
,
b
]
such that
∫
a
x
f
(
t
)
d
t
=
∫
x
b
f
(
t
)
d
t
\int_{a}^{x} f(t) dt = \int_{x}^{b} f(t) dt
∫
a
x
f
(
t
)
d
t
=
∫
x
b
f
(
t
)
d
t
.
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