Find all the continuous positive functions for such that where is a given real number
Chapter 5, Problem 122(choose chapter or problem)
Find all the continuous positive functions f(x), for \(0 \leq x \leq 1\), such that
\(\int_{0}^{1} f(x) d x=1\)
\(\int_{0}^{1} f(x) x d x=\alpha\)
\(\int_{0}^{1} f(x) x^{2} d x=\alpha^{2}\)
where \(\alpha\) is a given real number.
Text Transcription:
0 leq x leq 1
int_0^1 f(x) d x=1
int_0^1 f(x) x d x=alpha
int_0^1 f(x) x^2 d x=alpha^2
alpha
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