Today's calculation of Integral 343
Source: 1964 Putnam A2
June 12, 2008
calculusintegrationfunctioncalculus computations
Problem Statement
Find all continuous positive functions , for , 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 is given real number.