2026 IGCSE Additional Mathematics May/June 0606/21 Q11

The diagram shows part of the curve \(y=3+\dfrac1{1+x}\) and part of the curve \(y=4-\dfrac{12}{(1+x)^2}\).

The curve \(y=3+\dfrac1{1+x}\) meets the \(y\)-axis at the point \(A\).

The curve \(y=4-\dfrac{12}{(1+x)^2}\) meets the \(x\)-axis at the point \(C\).

The curves intersect at the point \(B\).

Find the area of the shaded region \(OABC\).

Give your answer in exact form.[10]