Edexcel C2 2012 June — Question 5

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2012
SessionJune
TopicAreas Between Curves

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f1ef99f0-4ad4-49d8-bee7-d5bb9cc84660-07_823_1081_267_404} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows the line with equation \(y = 10 - x\) and the curve with equation \(y = 10 x - x ^ { 2 } - 8\) The line and the curve intersect at the points \(A\) and \(B\), and \(O\) is the origin.
  1. Calculate the coordinates of \(A\) and the coordinates of \(B\). The shaded area \(R\) is bounded by the line and the curve, as shown in Figure 2.
  2. Calculate the exact area of \(R\).