Edexcel C2 2005 January — Question 8

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2005
SessionJanuary
TopicAreas Between Curves

8. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{13bca882-27da-40f2-99d8-4fdeb6629c4e-14_1102_1317_308_340}
\end{figure} The line with equation \(y = 3 x + 20\) cuts the curve with equation \(y = x ^ { 2 } + 6 x + 10\) at the points \(A\) and \(B\), as shown in Figure 2.
  1. Use algebra to find the coordinates of \(A\) and the coordinates of \(B\). The shaded region \(S\) is bounded by the line and the curve, as shown in Figure 2.
  2. Use calculus to find the exact area of \(S\).