8.
Figure 2
\includegraphics[max width=\textwidth, alt={}, center]{de11ae90-8693-4346-b195-1d01f2b164f5-03_791_972_276_303}
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 \(S\).