| 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 | Standard +0.2 This is a straightforward volumes of revolution question requiring standard integration techniques. Part (i) involves integrating (3x+1)^(-1/2) using a simple substitution or recognition, and part (ii) requires squaring the function to get (3x+1)^(-1) which integrates to a logarithm. Both are routine C3 exercises with no problem-solving insight needed, making this slightly easier than average. |
| Spec | 1.08d Evaluate definite integrals: between limits1.08e Area between curve and x-axis: using definite integrals4.08d Volumes of revolution: about x and y axes |
5.
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The diagram shows the curve with equation $y = \frac { 1 } { \sqrt { 3 x + 1 } }$.\\
The shaded region is bounded by the curve, the $x$-axis and the lines $x = 1$ and $x = 5$.\\
(i) Find the area of the shaded region.
The shaded region is rotated through four right angles about the $x$-axis.\\
(ii) Find the volume of the solid formed, giving your answer in the form $k \pi \ln 2$.\\
\hfill \mbox{\textit{OCR C3 Q5 [8]}}