Suppose that f : [-1, 1] → ℝ is continuous. Which of the following imply that f is identically zero on [-1, 1] ?
1
\(\int_{-1}^1 f(x) x^n d x=0\) for all n ≥ 0.
2
\(\int_{-1}^1 f(x) p(x) d x=0\) for all real polynomials p(x).
3
\(\int_{-1}^1 f(x) x^n d x=0\) for all n ≥ 0 odd.
4
\(\int_{-1}^1 f(x) x^n d x=0\) for all n ≥ 0 even.