6 The curve \(C\) has parametric equations
$$x = \mathrm { e } ^ { t } - 4 t + 3 , \quad y = 8 \mathrm { e } ^ { \frac { 1 } { 2 } t } , \quad \text { for } 0 \leqslant t \leqslant 2$$
- Find, in terms of e , the length of \(C\).
- Find, in terms of \(\pi\) and e , the area of the surface generated when \(C\) is rotated through \(2 \pi\) radians about the \(x\)-axis.