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Moldova Contests
Moldova National Olympiad
2007 Moldova National Olympiad
12.8
12.8
Part of
2007 Moldova National Olympiad
Problems
(1)
Integral identity-inequality
Source: Moldova MO 2007 12th grade day II problem 8
3/4/2007
Find all continuous functions
f
:
[
0
;
1
]
→
R
f\colon [0;1] \to R
f
:
[
0
;
1
]
→
R
such that
∫
0
1
f
(
x
)
d
x
=
2
∫
0
1
(
f
(
x
4
)
)
2
d
x
+
2
7
\int_{0}^{1}f(x)dx = 2\int_{0}^{1}(f(x^{4}))^{2}dx+\frac{2}{7}
∫
0
1
f
(
x
)
d
x
=
2
∫
0
1
(
f
(
x
4
)
)
2
d
x
+
7
2
calculus
integration
inequalities
function
real analysis
real analysis unsolved