| Exam Board | CAIE |
|---|
| Module | FP1 (Further Pure Mathematics 1) |
|---|
| Year | 2012 |
|---|
| Session | November |
|---|
| Topic | Parametric equations |
|---|
8 The curve \(C\) has parametric equations
$$x = \frac { 1 } { 3 } t ^ { 3 } - \ln t , \quad y = \frac { 4 } { 3 } t ^ { \frac { 3 } { 2 } }$$
for \(1 \leqslant t \leqslant 3\). Find the arc length of \(C\).
Find also the area of the surface generated when \(C\) is rotated through \(2 \pi\) radians about the \(x\)-axis.