2008 NJC Promo Q13
The diagram below shows the curve $C$ with equation given by
$x={{\text{e}}^{-t}}\cos 2t$, $y=\sin t$,
where $\frac{\pi }{2}\le t\le \pi $.
Write down the exact values of $a$ and $b$. By considering the integral $\int_{0}^{a}{x\,\text{d}y}$, show that the exact area of region $R$ is $\frac{3}{10}\left[ \left( \sqrt{2} \right){{\text{e}}^{-\frac{3\pi }{4}}}-{{\text{e}}^{-\pi }} \right]$.
[7]
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