Moderate -0.3 This is a standard volume of revolution question requiring integration of a polynomial after squaring. The setup is straightforward (identifying bounds and the function), and the integration involves routine expansion and application of the formula V = π∫y² dx. While it requires careful algebraic manipulation and exact arithmetic (5 marks suggests some working), it's a textbook exercise with no conceptual challenges beyond applying a memorized technique.
Please remember to show detailed reasoning in your answer
\includegraphics{figure_9}
The diagram shows the curve with equation \(y = (2x - 3)^2\). 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. [5]
\textbf{Please remember to show detailed reasoning in your answer}
\includegraphics{figure_9}
The diagram shows the curve with equation $y = (2x - 3)^2$. 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. [5]
\hfill \mbox{\textit{SPS SPS FM 2023 Q9 [5]}}