2025 IGCSE Additional Mathematics May/June 0606/13 Q8

The diagram shows part of the curve \(y=\dfrac3{x+1}-\dfrac{x-2}x\).

The points \(A\) and \(B\) lie on the curve such that the \(x\)-coordinate of \(A\) is \(1\) and the \(x\)-coordinate of \(B\) is \(2\).

1. Find the \(y\)-coordinates of \(A\) and \(B\).[1]
2. Show that the area of the shaded region enclosed by the line \(AB\) and the curve is \(\dfrac a4-\ln\dfrac b2\), where \(a\) and \(b\) are integers to be found.[7]