| Exam Board | CAIE |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2019 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration by Parts |
4 It is given that, for $n \geqslant 0$,
$$I _ { n } = \int _ { 0 } ^ { 1 } x ^ { n } \mathrm { e } ^ { x ^ { 3 } } \mathrm {~d} x$$
(i) Show that $I _ { 2 } = \frac { 1 } { 3 } ( \mathrm { e } - 1 )$.\\
(ii) Show that, for $n \geqslant 3$,
$$3 I _ { n } = \mathrm { e } - ( n - 2 ) I _ { n - 3 }$$
(iii) Hence find the exact value of $I _ { 8 }$.\\
\hfill \mbox{\textit{CAIE FP1 2019 Q4}}