If fff is continuous on [0,1][0,1][0,1] and ∫01f(x)xndx=0\int_0^1 f(x) x^n dx = 0∫01f(x)xndx=0 for all n≥0n \geq 0n≥0, what can we conclude about fff?
f(x)=1f(x) = 1f(x)=1
f(x)=0f(x) = 0f(x)=0
f(x)=xf(x) = xf(x)=x
No conclusion possible