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