| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Volumes of Revolution |
| Type | Multi-part: volume and area |
| Difficulty | Moderate -0.3 This is a straightforward volumes of revolution question requiring standard integration techniques. Part (i) involves integrating 1/(2x-1) using substitution (a routine C3 skill), and part (ii) applies the standard formula V = π∫y² dx with algebraic simplification to reach a given answer. Both parts are textbook exercises with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.08d Evaluate definite integrals: between limits4.08d Volumes of revolution: about x and y axes |
4. The finite region $R$ is bounded by the curve with equation $y = \frac { 1 } { 2 x - 1 }$, the $x$-axis and the lines $x = 1$ and $x = 2$.\\
(i) Find the exact area of $R$.\\
(ii) Show that the volume of the solid formed when $R$ is rotated through four right angles about the $x$-axis is $\frac { 1 } { 3 } \pi$.\\
\hfill \mbox{\textit{OCR C3 Q4 [8]}}