2019 ASRJC Promo Q8
(a)
The curve $C$ is defined by the equations
$x=2\text{cosec}t$, $y=5\cos t{{\sin }^{3}}t$, for $0<t\le \frac{\pi }{2}$.
The region $R$ is bounded by $C$, the $x$-axis and $x=4$ in the first quadrant. Find the exact area of the region $R$.
[6]
(b)
The diagram below shows the curves ${{C}_{1}}$ and ${{C}_{2}}$ with equations $y=2{{\left( x-1 \right)}^{2}}+3$ and $y=3{{x}^{2}}$ respectively. The region in the first quadrant enclosed by the curves and the $y$-axis is denoted by $S$. Find the volume of the solid generated when the region $S$ is rotated through $2\pi $ radians about the $y$-axis, giving your answer correct to $4$ decimal places.
[3]
Suggested Video And Handwritten Solutions
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