> 
> Prove that if $f: [0,1]\to \mathbb{R}$ and $g: [0,1]\to \mathbb{R}$ are continuous functions s.t.
>  $$\int\_0^1f(x)x^ndx=\int\_0^1g(x)x^ndx$$
>  for $n=1,2,...$
>  then $f=g$.
> 
> 
> 

I feel like I try to show that 
$$\int\_0^1(f(x)-g(x))x^ndx=0$$ and denote the sequence $h\_n(x)=(f(x)-g(x))x^n$.