TMUA 2021 · Paper 1 · Question 7

The function $f$ is such that $f (0) = 0$ , and $x f (x) > 0$ for all non-zero values of $x$ .

It is given that

\int_{- 2}^{2} f (x) d x = 4

and

\int_{- 2}^{2} ∣ f (x) ∣ d x = 8

Evaluate

\int_{- 2}^{0} f (∣ x ∣) d x

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