7. The diagram below shows part of a curve C with equation \(y = 1 + 3 x - \frac { 1 } { 2 } x ^ { 2 }\).
\includegraphics[max width=\textwidth, alt={}, center]{85570d22-3596-4795-93ed-bfe8d094e8b4-08_709_898_214_603}
i. The curve crosses the \(y\) axis at the point A . The straight line L is normal to the curve at A and meets the curve again at B . Find the equation of L and the \(x\) coordinate of the point B .
ii. The region \(R\) is bounded by the curve \(C\) and the line \(L\). Find the exact area of \(R\).