| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Area involving fractional powers |
| Difficulty | Moderate -0.3 This is a straightforward C2 integration question. Part (i) requires solving a simple equation (4x^(1/3) = x), which reduces to basic algebra. Part (ii) is a standard definite integration from 0 to 8 using power rule for fractional indices. Both parts are routine applications of core techniques with no conceptual challenges, making it slightly easier than average. |
| Spec | 1.08d Evaluate definite integrals: between limits1.08e Area between curve and x-axis: using definite integrals |
\includegraphics{figure_6}
The diagram shows the curve with equation $y = 4x^{\frac{1}{3}} - x$, $x \geq 0$.
The curve meets the $x$-axis at the origin and at the point $A$ with coordinates $(a, 0)$.
\begin{enumerate}[label=(\roman*)]
\item Show that $a = 8$. [3]
\item Find the area of the finite region bounded by the curve and the positive $x$-axis. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q6 [8]}}