2019 DHS Promo Q6

The shaded region \(R\) is bounded by the curves \(x=-3{{\mathrm{e}}^{-2y}}\), \(x=\frac{1}{2}-{{\mathrm{e}}^{2y}}\) and the \(x\)-axis is shown in the diagram below.

1. Find the exact region of the region \(R\).[5]
2. Find the volume of the solid or revolution formed when \(R\) is rotated through \(4\) right angles about the \(y\)-axis, giving your answer correct to \(2\) decimal places.[2]