<p>A curve ${C}$ has equation ${y = \frac{3 - x}{x - 1}}$.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Sketch ${C}$, stating the equations of the asymptotes.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">Find the exact volume of the solid generated when the region bounded by ${C}$, the ${x}$-axis and the line ${x=9}$ is rotated through ${2\pi}$ radians about the ${x}$-axis. Leave your answer in the form ${\pi (a + b \ln 2)}$, where ${a}$ and ${b}$ are constants to be determined.</div><p style="text-align: right;">[5]</p></li></ol>

A curve ${C}$ has equation ${y = \frac{3 - x}{x - 1}}$.

Sketch ${C}$, stating the equations of the asymptotes.

Find the exact volume of the solid generated when the region bounded by ${C}$, the ${x}$-axis and the line ${x=9}$ is rotated through ${2\pi}$ radians about the ${x}$-axis. Leave your answer in the form ${\pi (a + b \ln 2)}$, where ${a}$ and ${b}$ are constants to be determined.

2024 TJC P2 Q1

2024 TJC P2 Q1

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