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SEEMOUS
2011 SEEMOUS
Problem 1
Prove inequality
Prove inequality
Source: SEEMOUS
February 14, 2017
function
inequalities
real analysis
Integral inequality
Problem Statement
Let
f
:
[
0
,
1
]
→
R
f:[0,1]\rightarrow R
f
:
[
0
,
1
]
→
R
be a continuous function and n be an integer number,n>0.Prove that
∫
0
1
f
(
x
)
d
x
≤
(
n
+
1
)
∗
∫
0
1
x
n
∗
f
(
x
)
d
x
\int_0^1f(x)dx \le (n+1)*\int_0^1 x^n*f(x)dx
∫
0
1
f
(
x
)
d
x
≤
(
n
+
1
)
∗
∫
0
1
x
n
∗
f
(
x
)
d
x
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