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343

Part of 2008 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 343

Source: 1964 Putnam A2

6/12/2008
Find all continuous positive functions f(x) f(x), for 0≤x≤1 0\leq x\leq 1, such that \int_0^1 f(x)\ dx \equal{} 1 \int_0^1 xf(x)\ dx \equal{} \alpha \int_0^1 x^2f(x)\ dx \equal{} \alpha ^2 where α \alpha is given real number.
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