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Putnam
2003 Putnam
6
Putnam 2003 B6
Putnam 2003 B6
Source:
June 23, 2011
Putnam
function
integration
college contests
Problem Statement
Let
f
(
x
)
f(x)
f
(
x
)
be a continuous real-valued function defined on the interval
[
0
,
1
]
[0, 1]
[
0
,
1
]
. Show that
∫
0
1
∫
0
1
∣
f
(
x
)
+
f
(
y
)
∣
d
x
d
y
≥
∫
0
1
∣
f
(
x
)
∣
d
x
\int_0^1\int_0^1|f(x)+f(y)|dx \; dy \ge \int_0^1 |f(x)|dx
∫
0
1
∫
0
1
∣
f
(
x
)
+
f
(
y
)
∣
d
x
d
y
≥
∫
0
1
∣
f
(
x
)
∣
d
x
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