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Gresty Academy Paper 2 · Q15

Paper 2Logic & proofCalculus

Which of the following functions is a counterexample to the statement

If ∫01f(x) dx=0\displaystyle\int_0^1 f(x)\,\mathrm dx=0

then ∣f(x)∣<2|f(x)|<2 for all x∈[0,1]x\in[0,1]

Af(x)=0f(x)=0
Bf(x)=4x−2f(x)=4x-2
Cf(x)=sin⁡(2πx)f(x)=\sin(2\pi x)
Df(x)=1f(x)=1
Ef(x)=x2−xf(x)=x^2-x

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