The diagram above shows part of the graph of a curve $C$ given by $x=\frac{y}{y-1}$. The region

Question

The diagram above shows part of the graph of a curve $C$ given by $x=\frac{y}{y-1}$. The region $R$ is bounded by $C$ and the lines $y=x$ and $x=4$. Write down the equation of the curve obtained when $C$ is translated by $4$ units in the negative $x$-direction. Hence, or otherwise, write down also an expression for the volume $V$ of the solid formed when $R$ is rotated $2\pi $ radians about the line $x=4$ and find its numerical value, giving your answer correct to $3$ decimal places.[5]

Accepted Answer

(b) $x=\dfrac{y}{y-1}-4$ $V=\pi\int_{4/3}^{2}\left(\dfrac{y}{y-1}-4\right)^2\,\mathrm dy+\pi\int_2^4(y-4)^2\,\mathrm dy=12.802\text{ units}^3$

2009 NJC Promo Q10

2009 NJC Promo Q10

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