| Exam Board | CAIE |
|---|
| Module | FP1 (Further Pure Mathematics 1) |
|---|
| Year | 2016 |
|---|
| Session | June |
|---|
| Topic | Parametric equations |
|---|
A curve \(C\) has parametric equations
$$x = \mathrm { e } ^ { 2 t } \cos 2 t , \quad y = \mathrm { e } ^ { 2 t } \sin 2 t , \quad \text { for } - \frac { 1 } { 2 } \pi \leqslant t \leqslant \frac { 1 } { 2 } \pi .$$
Find the arc length of \(C\).
Find the area of the surface generated when \(C\) is rotated through \(2 \pi\) radians about the \(x\)-axis.