Standard +0.3 This is a straightforward volume of revolution question requiring integration of a polynomial. Students must set up the integral with correct limits (finding where the curve meets the x-axis at x=1.5), expand (2x-3)^4, integrate term-by-term, and apply limits. While it requires multiple steps, it's a standard C3 technique with no conceptual difficulty beyond the routine application of the volume formula πy² dx.
\includegraphics{figure_2}
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]
\includegraphics{figure_2}
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{OCR C3 2009 Q2 [5]}}