TMUA 2021 Paper 2 Q20 — Worked Solution

P2·Sequences & Series, Integration·7.0Official · 2021 · Q20

iterated-functionsmodulusarea-under-graph

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 .

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