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Putnam
1940 Putnam
A3
Putnam 1940 A3
Putnam 1940 A3
Source: Putnam 1940
February 22, 2022
Putnam
function
integration
calculus
Problem Statement
Let
a
a
a
be a real number. Find all real-valued functions
f
f
f
such that
∫
f
(
x
)
a
d
x
=
(
∫
f
(
x
)
d
x
)
a
\int f(x)^{a} dx=\left( \int f(x) dx \right)^{a}
∫
f
(
x
)
a
d
x
=
(
∫
f
(
x
)
d
x
)
a
when constants of integration are suitably chosen.
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