| Exam Board | CAIE |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2010 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Polar coordinates |
2 The curve $C$ has polar equation
$$r = a \left( 1 - \mathrm { e } ^ { - \theta } \right)$$
where $a$ is a positive constant and $0 \leqslant \theta < 2 \pi$.\\
(i) Draw a sketch of $C$.\\
(ii) Show that the area of the region bounded by $C$ and the lines $\theta = \ln 2$ and $\theta = \ln 4$ is
$$\frac { 1 } { 2 } a ^ { 2 } \left( \ln 2 - \frac { 13 } { 32 } \right)$$
\hfill \mbox{\textit{CAIE FP1 2010 Q2}}