Standard +0.3 This is a standard volumes of revolution question requiring the formula V = π∫y²dx, expansion of (1 + 1/(2√x))², and integration of polynomial and reciprocal terms. The algebra is slightly involved with the cross-term and the final answer requires logarithm manipulation, but it follows a well-practiced procedure with no novel insight required. Slightly easier than average due to its routine nature.
\includegraphics{figure_1}
Figure 1 shows part of the curve with equation \(y = 1 + \frac{1}{2\sqrt{x}}\). The shaded region \(R\), bounded by the curve, that \(x\)-axis and the lines \(x = 1\) and \(x = 4\), is rotated through \(360°\) about the \(x\)-axis. Using integration, show that the volume of the solid generated is \(\pi (5 + \frac{1}{2} \ln 2)\).
[8]
\includegraphics{figure_1}
Figure 1 shows part of the curve with equation $y = 1 + \frac{1}{2\sqrt{x}}$. The shaded region $R$, bounded by the curve, that $x$-axis and the lines $x = 1$ and $x = 4$, is rotated through $360°$ about the $x$-axis. Using integration, show that the volume of the solid generated is $\pi (5 + \frac{1}{2} \ln 2)$.
[8]
\hfill \mbox{\textit{Edexcel C4 Q26 [8]}}