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\includegraphics[max width=\textwidth, alt={}, center]{fa90db86-a73a-40db-b416-3c9f470fa207-4_762_848_255_646}
The diagram shows part of the curve \(y = - x ^ { 2 } + 8 x - 10\) which passes through the points \(A\) and \(B\). The curve has a maximum point at \(A\) and the gradient of the line \(B A\) is 2 .
- Find the coordinates of \(A\) and \(B\).
- Find \(\int y \mathrm {~d} x\) and hence evaluate the area of the shaded region.