3 The curve \(C\) has parametric equations $$x = \frac { 1 } { 2 } \mathrm { e } ^ { 2 t } - \frac { 1 } { 3 } t ^ { 3 } - \frac { 1 } { 2 } , \quad y = 2 \mathrm { e } ^ { t } ( t - 1 ) , \quad \text { for } 0 \leqslant t \leqslant 1 .$$ Find the exact length of \(C\) .
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