| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Volumes of Revolution |
| Type | Volume with exact answer required |
| Difficulty | Standard +0.3 This is a straightforward volumes of revolution question requiring students to apply the standard formula V = π∫y²dx, simplify the algebraic expression (3x+1)²/x, and integrate term-by-term. While it involves logarithmic integration, this is standard C3 material with no conceptual challenges beyond routine technique application. |
| Spec | 1.08d Evaluate definite integrals: between limits4.08d Volumes of revolution: about x and y axes |
2.
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The diagram shows the curve with equation $y = \frac { 3 x + 1 } { \sqrt { x } } , x > 0$.\\
The shaded region is bounded by the curve, the $x$-axis and the lines $x = 1$ and $x = 3$.\\
Find the volume of the solid formed when the shaded region is rotated through four right angles about the $x$-axis, giving your answer in the form $\pi ( a + \ln b )$, where $a$ and $b$ are integers.\\
\hfill \mbox{\textit{OCR C3 Q2 [6]}}