The problem statement, all variables and given/known data Suppose f: [0,1] --> R is continuous and [tex]\int_0^1 f(x) x^n \, dx = 0[/tex] for all n = 0, 1, ... Prove that f(x) = 0. The attempt at a solution There's a hint that says: Prove that [tex]\int_0^1 (f(x))^2 \, dx = 0.[/tex] I don't know how to prove this hint and I don't know how that would help in determining what f is. Any tips?