(3) \( (10\%) \) \( f \) is continuous on \( [0,1] \) and if \( \int_0^1 f(x)x^n dx = 0 \) for any \( n = 0,1,2,\ldots \), prove that \( f(x) = 0 \) on \( [0,1] \).
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(3) \( (10\%) \) \( f \) is continuous on \( [0,1] \) and if \( \int_0^1 f(x)x^n dx = 0 \) for any \( n = 0,1,2,\ldots \), prove that \( f(x) = 0 \) on \( [0,1] \).