| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Area under curve with fractional/negative powers or roots |
| Difficulty | Moderate -0.3 This is a straightforward application of standard integration techniques for area and volume of revolution. Part (i) requires integrating (3x+2)^(-1/2) using the reverse chain rule, and part (ii) uses the standard volume formula with y². Both are routine C3 exercises with no conceptual challenges, though the algebra requires care. Slightly easier than average due to the direct application of formulas. |
| 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 |
\includegraphics{figure_6}
The diagram shows the curve with equation $y = \frac{1}{\sqrt{3x + 2}}$. The shaded region is bounded by the curve and the lines $x = 0$, $x = 2$ and $y = 0$.
\begin{enumerate}[label=(\roman*)]
\item Find the exact area of the shaded region. [4]
\item The shaded region is rotated completely about the $x$-axis. Find the exact volume of the solid formed, simplifying your answer. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q6 [9]}}