Edexcel C2 2013 June — Question 6

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2013
SessionJune
TopicArea Under & Between Curves

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1c51b071-5cb1-4841-b031-80bde9027433-10_697_1182_210_386} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows a sketch of part of the curve \(C\) with equation $$y = x ( x + 4 ) ( x - 2 )$$ The curve \(C\) crosses the \(x\)-axis at the origin \(O\) and at the points \(A\) and \(B\).
  1. Write down the \(x\)-coordinates of the points \(A\) and \(B\). The finite region, shown shaded in Figure 3, is bounded by the curve \(C\) and the \(x\)-axis.
  2. Use integration to find the total area of the finite region shown shaded in Figure 3.