| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2010 |
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| Session | November |
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| Topic | Reduction Formulae |
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5 Let \(I _ { n } = \int _ { 0 } ^ { 1 } ( 1 - x ) ^ { n } \sin x \mathrm {~d} x\) for \(n \geqslant 0\). Show that
$$I _ { n + 2 } = 1 - ( n + 1 ) ( n + 2 ) I _ { n }$$
Hence find the value of \(I _ { 6 }\), correct to 4 decimal places.