0606 P12 - Nov 2021 - Q10 - 8 marks
8029
The diagram shows the graph of the curve
\(y=\frac{1}{(x+2)^2}+\frac{3}{x+2}\)
for \(x\gt -2\). The points \(A\) and \(B\) lie on the curve such that the \(x\)-coordinates of \(A\) and \(B\) are \(-1\) and \(2\) respectively.
(a) Find the exact \(y\)-coordinates of \(A\) and of \(B\).
(b) Find the area of the shaded region enclosed by the line \(AB\) and the curve, giving your answer in the form \(\frac pq-\ln r\), where \(p\), \(q\) and \(r\) are integers.
