The number of all continuous positive fu...

The number of all continuous positive functions `f` defined on the interval `[0, 1]` such that `int_0^1\ f(x)dx = 1;\ int_0^1\ f(x)* x\ d x = alpha and int_0^1\ f(x)*x^2\ dx= alpha^2 `(where `alpha` is a given real number)

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