| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Volumes of Revolution |
| Type | Volume requiring substitution or integration by parts |
| Difficulty | Challenging +1.2 This is a standard C4 volumes of revolution question requiring integration by parts (part a) followed by applying the volume formula with straightforward algebraic manipulation. Part (a) is routine IBP practice, and part (b) requires squaring y=√x sin 2x to get x sin²2x, then using the double angle formula and integrating—all standard techniques for this topic. The question is slightly above average difficulty due to the multi-step nature and need to apply the result from part (a), but follows predictable C4 patterns without requiring novel insight. |
| Spec | 1.08i Integration by parts4.08d Volumes of revolution: about x and y axes |
Question 8:
$8 \mid 3$
$32 \mid 17.599$8.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{0c4a3759-ecaa-47c3-a071-ce25fd11159f-28_680_1266_118_482}
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\caption{Figure 3}
\end{center}
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\begin{enumerate}[label=(\alph*)]
\item Find $\int x \cos 4 x d x$
Figure 3 shows part of the curve with equation $y = \sqrt { x } \sin 2 x , \quad x \geqslant 0$\\
The finite region $R$, shown shaded in Figure 3, is bounded by the curve, the $x$-axis and the line with equation $x = \frac { \pi } { 4 }$
The region $R$ is rotated through $2 \pi$ radians about the $x$-axis to form a solid of revolution.
\item Find the exact value of the volume of this solid of revolution, giving your answer in its simplest form.\\
(Solutions based entirely on graphical or numerical methods are not acceptable.)
\includegraphics[max width=\textwidth, alt={}, center]{0c4a3759-ecaa-47c3-a071-ce25fd11159f-32_2630_1828_121_121}
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 2018 Q8 [9]}}