Figure 1 shows a sketch of part of the curve with equation $$\(y=\mathrm{e}^{0.5 x}-2\)$$ The region $$\(R\)$$, shown shaded in Figure 1, is bounded by the curve, the $$\(x\)$$-axis and the $$\(y\)$$-axis. The region $$\(R\)$$ is rotated $$\(360^{\circ}\)$$ about the $$\(x\)$$-axis to form a solid of revolution. Show that the volume of this solid can be written in the form $$\(a \ln 2+b\)$$, where $$\(a\)$$ and $$\(b\)$$ are constants to be found. (6)

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