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Putnam
2014 Putnam
2
Putnam 2014 B2
Putnam 2014 B2
Source:
December 8, 2014
Putnam
function
integration
real analysis
absolute value
Putnam calculus
Putnam 2014
Problem Statement
Suppose that
f
f
f
is a function on the interval
[
1
,
3
]
[1,3]
[
1
,
3
]
such that
−
1
≤
f
(
x
)
≤
1
-1\le f(x)\le 1
−
1
≤
f
(
x
)
≤
1
for all
x
x
x
and
∫
1
3
f
(
x
)
d
x
=
0.
\displaystyle \int_1^3f(x)\,dx=0.
∫
1
3
f
(
x
)
d
x
=
0.
How large can
∫
1
3
f
(
x
)
x
d
x
\displaystyle\int_1^3\frac{f(x)}x\,dx
∫
1
3
x
f
(
x
)
d
x
be?
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