MathDB
Problems
Contests
National and Regional Contests
Romania Contests
Romania - Local Contests
Bogdan Stan
2012 Bogdan Stan
2
Integral functional relation
Integral functional relation
Source:
November 25, 2019
function
Find all functions
calculus
integration
Problem Statement
Find the continuous functions
f
:
[
0
,
1
3
]
⟶
(
0
,
∞
)
f:\left[ 0,\frac{1}{3} \right] \longrightarrow (0,\infty )
f
:
[
0
,
3
1
]
⟶
(
0
,
∞
)
that satisfy the functional relation
54
∫
0
1
/
3
f
(
x
)
d
x
+
32
∫
0
1
/
3
d
x
x
+
f
(
x
)
=
21.
54\int_0^{1/3} f(x)dx +32\int_0^{1/3} \frac{dx}{\sqrt{x+f(x)}} =21.
54
∫
0
1/3
f
(
x
)
d
x
+
32
∫
0
1/3
x
+
f
(
x
)
d
x
=
21.
Cristinel Mortici
Back to Problems
View on AoPS