4 The region bounded by the curve \(\mathrm { y } = 2 \mathrm { e } ^ { \frac { 1 } { 2 } \mathrm { x } }\) for \(0 \leqslant x \leqslant 2\), the \(x\)-axis, the \(y\)-axis and the line \(x = 2\), is occupied by a uniform lamina.

1. Find the exact value of the \(y\)-coordinate of the centre of mass of the lamina. As shown in the diagram below, a uniform lamina occupies the closed region bounded by the \(x\)-axis, the \(y\)-axis and the curve \(\mathrm { y } = \mathrm { f } ( \mathrm { x } )\) where $$f ( x ) = \begin{cases} 2 \mathrm { e } ^ { \frac { 1 } { 2 } x } & 0 \leqslant x \leqslant 2
   \frac { 2 } { 3 } ( 5 - x ) \mathrm { e } & 2 \leqslant x \leqslant 5 . \end{cases}$$ \includegraphics[max width=\textwidth, alt={}, center]{27b790da-800f-4f5e-8f63-d52159efb48e-4_863_1179_762_443}
2. Find the exact value of the \(x\)-coordinate of the centre of mass of the lamina.