6 In this question you must show detailed reasoning.
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The diagram shows the curves \(y = \sqrt { 2 x + 9 }\) and \(y = 4 \mathrm { e } ^ { - 2 x } - 1\) which intersect on the \(y\)-axis. The shaded region is bounded by the curves and the \(x\)-axis.
Determine the area of the shaded region, giving your answer in the form \(p + q \ln 2\) where \(p\) and \(q\) are constants to be determined.