8.
\begin{figure}[h]
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\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.
- 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.
- Use calculus to find the exact area of \(S\).