TMUA 2016 Paper 2 Q18 — Worked Solution

P2·Integration, Logic & Quantifiers·7.0Official · 2016 · Q18

counterexampleintegral-inequalityodd-functions

Consider this statement about a function

f (x)

(∗)

(f (x))^{2} \leq 1

for all

- 1 \leq x \leq 1

then

\int_{- 1}^{1} (f (x))^{2} d x \leq \int_{- 1}^{1} f (x) d x

Which one of the following functions provides a counterexample to (∗) ?

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