SPS SPS FM 2023 January — Question 9

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2023
SessionJanuary
TopicVolumes of Revolution

9. Please remember to show detailed reasoning in your answer
\includegraphics[max width=\textwidth, alt={}, center]{d193321f-0471-48cd-b954-4a7330777491-20_467_817_239_639} The diagram shows the curve with equation \(y = ( 2 x - 3 ) ^ { 2 }\). The shaded region is bounded by the curve and the lines \(x = 0\) and \(y = 0\). Find the exact volume obtained when the shaded region is rotated completely about the \(x\)-axis.
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