Edexcel C2 — Question 7

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
TopicAreas Between Curves

7. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{1425d933-47e3-4a12-bcab-fd2ca41827e2-3_531_1216_998_189}
\end{figure} Fig. 2 shows the line with equation \(y = x + 1\) and the curve with equation \(y = 6 x - x ^ { 2 } - 3\).
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 region \(R\) is bounded by the line and the curve.
  2. Calculate the area of \(R\).