TMUA 2021 · Paper 2 · Question 20

A sequence of functions $f_{1}, f_{2}, f_{3}, \dots$ is defined by

f_{1} (x) = ∣ x ∣

f_{n + 1} (x) = ∣ f_{n} (x) + x ∣ for n \geq 1

Find the value of

\int_{- 1}^{1} f_{99} (x) d x