2024 IGCSE Additional Mathematics October/November 0606/11 Q11

The diagram shows part of the curve \(y=4+2\sin3x\) and the straight line \(AB\). The points \(A\) and \(B\) lie on the curve. The \(x\)-coordinate of \(A\) is \(\dfrac\pi{18}\) and the \(x\)-coordinate of \(B\) is \(\dfrac\pi3\). Find the area of the shaded region, giving your answer in exact form.[9]