| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Volumes of Revolution |
| Type | Multi-part: volume and area |
| Difficulty | Moderate -0.3 This is a straightforward C4 question testing standard techniques: trapezium rule application (routine calculation with 4 strips), concavity reasoning for over/under-estimate, and volume of revolution using the standard formula V = π∫y² dx. All parts are textbook exercises requiring method recall rather than problem-solving, though the multi-part structure and 12 total marks place it slightly below average difficulty. |
| Spec | 1.09f Trapezium rule: numerical integration4.08d Volumes of revolution: about x and y axes |
\includegraphics{figure_2}
Figure 2 shows part of the curve with equation $y = x^2 + 2$.
The finite region $R$ is bounded by the curve, the $x$-axis and the lines $x = 0$ and $x = 2$.
\begin{enumerate}[label=(\alph*)]
\item Use the trapezium rule with 4 strips of equal width to estimate the area of $R$. [5]
\item State, with a reason, whether your answer in part $(a)$ is an under-estimate or over-estimate of the area of $R$. [1]
\item Using integration, find the volume of the solid generated when $R$ is rotated through $360°$ about the $x$-axis, giving your answer in terms of $\pi$. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q25 [12]}}