| Exam Board | CAIE |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2017 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Reduction Formulae |
6 Let $I _ { n } = \int _ { 0 } ^ { \frac { 1 } { 2 } \pi } x ^ { n } \sin x \mathrm {~d} x$.\\
(i) Prove that, for $n \geqslant 2$,
$$I _ { n } + n ( n - 1 ) I _ { n - 2 } = n \left( \frac { 1 } { 2 } \pi \right) ^ { n - 1 } .$$
(ii) Calculate the exact value of $I _ { 1 }$ and deduce the exact value of $I _ { 3 }$.\\
\hfill \mbox{\textit{CAIE FP1 2017 Q6}}