Figure 2 shows a sketch of the curve with parametric equations $$\[ x=\sqrt{9-4 t} \quad y=\frac{t^{3}}{\sqrt{9+4 t}} \quad 0 \leqslant t \leqslant \frac{9}{4} \]$$ The curve touches the $$\(x\)$$-axis when $$\(t=0\)$$ and meets the $$\(y\)$$-axis when $$\(t=\frac{9}{4}\)$$ The region $$\(R\)$$, shown shaded in Figure 2, is bounded by the curve, the $$\(x\)$$-axis and the $$\(y\)$$-axis. (a) Show that the area of $$\(R\)$$ is given by $$\[ K \int_{0}^{\frac{9}{4}} \frac{t^{3}}{\sqrt{81-16 t^{2}}} \mathrm{~d} t \]$$ where $$\(K\)$$ is a constant to be found. (4) (b) Using the substitution $$\(u=81-16 t^{2}\)$$, or otherwise, find the exact area of $$\(R\)$$. (Solutions relying on calculator technology are not acceptable.) (6)

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