| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard Integrals and Reverse Chain Rule |
| Type | Find curve equation from derivative (extended problem with normals, stationary points, or further geometry) |
| Difficulty | Moderate -0.8 This is a straightforward C2 integration question requiring basic power rule integration (rewriting x^{-3} and integrating to get x^{-2}) and using a point to find the constant. Part (ii) is routine definite integration. Both parts are standard textbook exercises with no problem-solving insight required, making this easier than average. |
| Spec | 1.08a Fundamental theorem of calculus: integration as reverse of differentiation1.08d Evaluate definite integrals: between limits1.08e Area between curve and x-axis: using definite integrals |
5. The curve $y = \mathrm { f } ( x )$ passes through the point $P ( - 1,3 )$ and is such that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 4 } { x ^ { 3 } } , \quad x \neq 0$$
(i) Find $\mathrm { f } ( x )$.\\
(ii) Show that the area of the finite region bounded by the curve $y = \mathrm { f } ( x )$, the $x$-axis and the lines $x = 1$ and $x = 4$ is $4 \frac { 1 } { 2 }$.\\
\hfill \mbox{\textit{OCR C2 Q5 [8]}}