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Putnam
2016 Putnam
A3
A3
Part of
2016 Putnam
Problems
(1)
Putnam 2016 A3
Source:
12/4/2016
Suppose that
f
f
f
is a function from
R
\mathbb{R}
R
to
R
\mathbb{R}
R
such that
f
(
x
)
+
f
(
1
−
1
x
)
=
arctan
x
f(x)+f\left(1-\frac1x\right)=\arctan x
f
(
x
)
+
f
(
1
−
x
1
)
=
arctan
x
for all real
x
≠
0.
x\ne 0.
x
=
0.
(As usual,
y
=
arctan
x
y=\arctan x
y
=
arctan
x
means
−
π
/
2
<
y
<
π
/
2
-\pi/2<y<\pi/2
−
π
/2
<
y
<
π
/2
and
tan
y
=
x
.
\tan y=x.
tan
y
=
x
.
) Find
∫
0
1
f
(
x
)
d
x
.
\int_0^1f(x)\,dx.
∫
0
1
f
(
x
)
d
x
.
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