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Miklós Schweitzer
1973 Miklós Schweitzer
6
Miklos Schweitzer 1973_6
Miklos Schweitzer 1973_6
Source:
November 12, 2008
function
integration
search
real analysis
real analysis unsolved
Problem Statement
If
f
f
f
is a nonnegative, continuous, concave function on the closed interval
[
0
,
1
]
[0,1]
[
0
,
1
]
such that
f
(
0
)
=
1
f(0)=1
f
(
0
)
=
1
, then
∫
0
1
x
f
(
x
)
d
x
≤
2
3
[
∫
0
1
f
(
x
)
d
x
]
2
.
\int_0^1 xf(x)dx \leq \frac 23 \left[ %Error. "diaplaymath" is a bad command. \int_0^1 f(x)dx \right]^2.
∫
0
1
x
f
(
x
)
d
x
≤
3
2
[
∫
0
1
f
(
x
)
d
x
]
2
.
Z. Daroczy
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