<p>A function $\mathrm{f}$ is defined by</p>
<p style="text-align: center">$\mathrm{f}(x)\left\{ \begin{matrix}\frac{6}{x-4}\,\,\,\,\,\,\,\,\,\,\mathrm{for }x<-2, & \\-\left| 1+x \right|\,\,\,\,\,\,\,\,\,\,\mathrm{for}\,-2\le x<1, & \\{{x}^{2}}-x-2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\mathrm{for}\,x>1. & \\\end{matrix} \right.$</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Sketch the graph of $\mathrm{f}$.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">Evaluate exactly $\int_{-3}^{4}{\left| \mathrm{f}(x) \right|\mathrm{d}x}$.</span></div><p style="text-align: right;">[4]</p></li></ol>

$\mathrm{f}(x)\left\{ \begin{matrix}\frac{6}{x-4}\,\,\,\,\,\,\,\,\,\,\mathrm{for }x<-2, & \\-\left| 1+x \right|\,\,\,\,\,\,\,\,\,\,\mathrm{for}\,-2\le x<1, & \\{{x}^{2}}-x-2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\mathrm{for}\,x>1. & \\\end{matrix} \right.$

Evaluate exactly $\displaystyle\displaystyle \int_{-3}^{4}{\left| \mathrm{f}(x) \right|\mathrm{d}x}$.

2019 ASRJC P1 Q6

2019 ASRJC P1 Q6

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