The diagram below shows the curve $C$ with equation given by $x={{\mathrm{e}}^{-t}}\cos 2t$, $y=\sin

Question

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

Accepted Answer

$\frac{3}{10}\left[\sqrt{2}\, e^{-\frac{3}{4}\pi} - e^{-\pi}\right]$

2008 NJC Promo Q13

2008 NJC Promo Q13

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