2026 MAY TZA P2 Q4

Consider the function \(g\) defined as \(g(x) = x^3 - 3x + 2\sin{x}\), where \(x \in \mathbb{R}\).
The graph of \(g\) has a local maximum point \(\mathrm{A}\) and a local minimum at point \(\mathrm{B}\). The line \( (\mathrm{AB}) \) passes through the origin \(\mathrm{O}\) at \( (0,0) \).
The region \(\mathrm{R}\) is enclosed by the graph of \(g\) and the line segment \([\mathrm{OB}]\), as shown on the following diagram.

1. Find the coordinates of point \(\mathrm{A}\) and the coordinates of point \(\mathrm{B}\).

   [2]

2. Find the area of \(\mathrm{R}\).

   [5]