5 Th cn e \(C\) has parametric equations
$$x = \mathrm { e } ^ { t } - 4 t + 3 \quad y = 8 \mathrm { e } ^ { \frac { 1 } { 2 } t } , \quad \text { f } \mathbf { D } \quad 0 \leqslant t \leqslant 2$$
- 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 ab the \(x\)-ax s.
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