IB AA HL May 2026 P2 TZA 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 at point \(A\) and a local minimum at point \(B\). The line \((AB)\) passes through the origin \(O\) at \((0,0)\).

The region \(R\) is enclosed by the graph of \(g\) and the line segment \([OB]\), as shown on the following diagram.

1. Find the coordinates of point \(A\) and the coordinates of point \(B\).[2]
2. Find the area of \(R\).[5]