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Putnam
1958 February Putnam
B7
Putnam 1958 February B7
Putnam 1958 February B7
Source: Putnam 1958 February
July 19, 2022
Putnam
continuity
Integral
Problem Statement
Prove that if
f
(
x
)
f(x)
f
(
x
)
is continuous for
a
≤
x
≤
b
a\leq x \leq b
a
≤
x
≤
b
and
∫
a
b
x
n
f
(
x
)
d
x
=
0
\int_{a}^{b} x^n f(x) \, dx =0
∫
a
b
x
n
f
(
x
)
d
x
=
0
for
n
=
0
,
1
,
2
,
…
,
n=0,1,2, \ldots,
n
=
0
,
1
,
2
,
…
,
then
f
(
x
)
f(x)
f
(
x
)
is identically zero on
a
≤
x
≤
b
.
a \leq x \leq b.
a
≤
x
≤
b
.
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