| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2013 |
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| Session | November |
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| Topic | Reduction Formulae |
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4 It is given that
$$I _ { n } = \int _ { 0 } ^ { 1 } \frac { x ^ { n } } { \sqrt { } ( 1 + 2 x ) } \mathrm { d } x$$
Show that, for \(n \geqslant 1\),
$$( 2 n + 1 ) I _ { n } = \sqrt { } 3 - n I _ { n - 1 }$$
Show that
$$I _ { 3 } = \frac { 2 } { 35 } ( \sqrt { } 3 + 1 )$$