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Putnam
1964 Putnam
A2
Putnam 1964 A2
Putnam 1964 A2
Source: Putnam 1964
March 5, 2022
Putnam
integration
system of equations
Problem Statement
Find all continuous positive functions
f
(
x
)
f(x)
f
(
x
)
, for
0
≤
x
≤
1
0\leq x \leq 1
0
≤
x
≤
1
, such that
∫
0
1
f
(
x
)
d
x
=
1
,
\int_{0}^{1} f(x)\; dx =1,
∫
0
1
f
(
x
)
d
x
=
1
,
∫
0
1
x
f
(
x
)
d
x
=
α
,
\int_{0}^{1} xf(x)\; dx =\alpha,
∫
0
1
x
f
(
x
)
d
x
=
α
,
∫
0
1
x
2
f
(
x
)
d
x
=
α
2
,
\int_{0}^{1} x^2 f(x)\; dx =\alpha^2,
∫
0
1
x
2
f
(
x
)
d
x
=
α
2
,
where
α
\alpha
α
is a given real number.
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