Edexcel C2 2006 January — Question 9

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2006
SessionJanuary
TopicAreas Between Curves

9. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 3} \includegraphics[alt={},max width=\textwidth]{84b2d36b-c112-4d35-84a1-bc2b707f162d-14_545_922_312_497}
\end{figure} Figure 3 shows the shaded region \(R\) which is bounded by the curve \(y = - 2 x ^ { 2 } + 4 x\) and the line \(y = \frac { 3 } { 2 }\). The points \(A\) and \(B\) are the points of intersection of the line and the curve. Find
  1. the \(x\)-coordinates of the points \(A\) and \(B\),
  2. the exact area of \(R\).