6. In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{08756c4b-6619-42da-ac8a-2bf065c01de8-18_650_938_413_504}
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\caption{Figure 2}
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Figure 2 shows a sketch of the curve with equation
$$y = \frac { 16 \sin 2 x } { ( 3 + 4 \sin x ) ^ { 2 } } \quad 0 \leqslant x \leqslant \frac { \pi } { 2 }$$
The region \(R\), shown shaded in Figure 2, is bounded by the curve, the \(x\)-axis and the line with equation \(x = \frac { \pi } { 6 }\)
Using the substitution \(u = 3 + 4 \sin x\), show that the area of \(R\) can be written in the form \(a + \ln b\), where \(a\) and \(b\) are rational constants to be found.