| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2010 |
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| Session | June |
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| Topic | Parametric equations |
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4 The parametric equations of a curve are
$$x = \cos t + t \sin t , \quad y = \sin t - t \cos t$$
The arc of the curve joining the point where \(t = 0\) to the point where \(t = \frac { 1 } { 2 } \pi\) is rotated about the \(x\)-axis through one complete revolution. Find the area of the surface generated, leaving your result in terms of \(\pi\).