| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Volumes of Revolution |
| Type | Rotation about x-axis: rational or reciprocal function |
| Difficulty | Standard +0.2 Part (a) is a standard volume of revolution question requiring rewriting the function, squaring it, and integrating—routine C3 technique. Part (b) is a textbook application of Simpson's rule with 4 strips. Both parts are straightforward applications of standard methods with no problem-solving or insight required, making this slightly easier than average. |
| Spec | 1.08d Evaluate definite integrals: between limits1.09f Trapezium rule: numerical integration |
\begin{enumerate}[label=(\alph*)]
\item \includegraphics{figure_4a}
The diagram shows the curve $y = \frac{2}{\sqrt{x}}$. The region $R$, shaded in the diagram, is bounded by the curve and by the lines $x = 1$, $x = 5$ and $y = 0$. The region $R$ is rotated completely about the $x$-axis. Find the exact volume of the solid formed. [4]
\item Use Simpson's rule, with 4 strips, to find an approximate value for
$$\int_1^5 \sqrt{(x^2 + 1)} \, dx,$$
giving your answer correct to 3 decimal places. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q4 [8]}}