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2022 IMC
1
1
Part of
2022 IMC
Problems
(1)
Welcome back to Blagoevgrad with a walk in the park
Source: IMC 2022 Day 1 Problem 1
8/5/2022
Let
f
:
[
0
,
1
]
→
(
0
,
∞
)
f: [0,1] \to (0, \infty)
f
:
[
0
,
1
]
→
(
0
,
∞
)
be an integrable function such that
f
(
x
)
f
(
1
−
x
)
=
1
f(x)f(1-x) = 1
f
(
x
)
f
(
1
−
x
)
=
1
for all
x
∈
[
0
,
1
]
x\in [0,1]
x
∈
[
0
,
1
]
. Prove that
∫
0
1
f
(
x
)
d
x
≥
1
\int_0^1f(x)dx \geq 1
∫
0
1
f
(
x
)
d
x
≥
1
.
function
inequalities
integration
calculus
IMC 2022