The curve \(C\) has equation \(y=\mathrm{e}^{-2 x}\). Find, giving your answers correct to 3 significant figures,
(i) the mean value of \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) over the interval \(0 \leqslant x \leqslant 2\),

(ii) the coordinates of the centroid of the region bounded by \(C, x=0, x=2\) and \(y=0\).