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Lebl-Basic-Analysis-I
· Problem 5.2.4
The Riemann Integral
Mathematics · mean-value-theorem-integrals
Problem
Prove the mean value theorem for integrals: If
f
:
[
a
,
b
]
→
R
f : [a,b] \to \mathbb{R}
f
:
[
a
,
b
]
→
R
is continuous, then there exists a
c
∈
[
a
,
b
]
c \in [a,b]
c
∈
[
a
,
b
]
such that
∫
a
b
f
=
f
(
c
)
(
b
−
a
)
\int_a^b f = f(c)(b-a)
∫
a
b
f
=
f
(
c
)
(
b
−
a
)
.
Related theory
Mean Value Theorem And Rolle S Theorem
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