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IMC
2005 IMC
3
IMC 2005 day 1 pb 3
IMC 2005 day 1 pb 3
Source: Peter
July 26, 2005
integration
inequalities
LaTeX
IMC
college contests
Problem Statement
3)
f
f
f
cont diff,
R
→
]
0
,
+
∞
[
R\rightarrow ]0,+\infty[
R
→
]
0
,
+
∞
[
, prove
∣
∫
0
1
f
3
−
f
(
0
)
2
∫
0
1
f
∣
≤
max
[
0
,
1
]
∣
f
′
∣
(
∫
0
1
f
)
2
|\int_{0}^{1}f^{3}-{f(0)}^{2}\int_{0}^{1}f| \leq \max_{[0,1]} |f'|(\int_{0}^{1}f)^{2}
∣
∫
0
1
f
3
−
f
(
0
)
2
∫
0
1
f
∣
≤
max
[
0
,
1
]
∣
f
′
∣
(
∫
0
1
f
)
2
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