2019 YIJC P1 Q3
The function $\text{f}$ is defined by
$\text{f}\left( x \right)=\left\{ \begin{matrix}
{{\left( x-2a \right)}^{2}}\text{ for }0\le x<2a, \\
2ax-4{{a}^{2}}\text{ for }2a\le x<4a, \\
\end{matrix} \right.$
Where $a$ is a positive real constant and that $\text{f}\left( x+4a \right)=\text{f}\left( x \right)$ for all real values of $x$.
(i)
Sketch the graph of $y=\text{f}\left( x \right)$ for $-3a\le x\le 8a$.
[3]
(ii)
Hence find the value of $\int\limits_{-2a}^{8a}{\text{f}\left( \left| x \right| \right)}\text{ d}x$ in terms of $a$.
[3]
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