Figure 2 Figure 2 shows a sketch of part of the curve $$\(C\)$$ with equation $$\(y^{2}=8 x\)$$ and part of the line $$\(l\)$$ with equation $$\(x=18\)$$ The region $$\(R\)$$, shown shaded in Figure 2, is bounded by $$\(C\)$$ and $$\(l\)$$ Show that the perimeter of $$\(R\)$$ is given by $$\[ \alpha+2 \int_{0}^{\beta} \sqrt{1+\frac{y^{2}}{16}} d y \]$$ where $$\(\alpha\)$$ and $$\(\beta\)$$ are positive constants to be determined. (3)

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