| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2008 |
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| Session | November |
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| Topic | Parametric equations |
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1 The curve \(C\) is defined parametrically by
$$x = t ^ { 4 } - 4 \ln t , \quad y = 4 t ^ { 2 }$$
Show that the length of the arc of \(C\) from the point where \(t = 2\) to the point where \(t = 4\) is
$$240 + 4 \ln 2 .$$