Edexcel C12 2019 June — Question 16

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2019
SessionJune
TopicAreas Between Curves

16. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{de511cb3-35c7-4225-b459-a136b6304b78-48_855_780_267_580} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} Figure 4 shows a sketch of the curve with equation \(y = 2 x ^ { 2 } - 11 x + 12\). The curve crosses the \(y\)-axis at the point \(A\) and crosses the \(x\)-axis at the points \(B\) and \(C\).
  1. Find the coordinates of the points \(A , B\) and \(C\). The point \(D\) lies on the curve such that the line \(A D\) is parallel to the \(x\)-axis. The finite region \(R\), shown shaded in Figure 4, is bounded by the curve, the line \(A C\) and the line \(A D\).
  2. Use algebraic integration to find the exact area of \(R\).