Edexcel C12 2016 January — Question 16

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2016
SessionJanuary
TopicAreas Between Curves

16. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{88ed9a17-97a5-4548-80bb-70b4b901a39d-19_835_922_303_513} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} The straight line \(l\) with equation \(y = \frac { 1 } { 2 } x + 1\) cuts the curve \(C\), with equation \(y = x ^ { 2 } - 4 x + 3\), at the points \(P\) and \(Q\), as shown in Figure 2
  1. Use algebra to find the coordinates of the points \(P\) and \(Q\). The curve \(C\) crosses the \(x\)-axis at the points \(T\) and \(S\).
  2. Write down the coordinates of the points \(T\) and \(S\). The finite region \(R\) is shown shaded in Figure 2. This region \(R\) is bounded by the line segment \(P Q\), the line segment \(T S\), and the \(\operatorname { arcs } P T\) and \(S Q\) of the curve.
  3. Use integration to find the exact area of the shaded region \(R\).