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 \(C\).
- 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 \(A D\).
- Use algebraic integration to find the exact area of \(R\).