| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard Integrals and Reverse Chain Rule |
| Type | Definite integral with exponentials |
| Difficulty | Moderate -0.5 Both parts are straightforward applications of standard integration techniques. Part (i) requires reverse chain rule for exponentials (routine C3 skill), and part (ii) simplifies to polynomial integration after algebraic manipulation. These are textbook exercises testing basic competency rather than problem-solving, making them slightly easier than average A-level questions. |
| Spec | 1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)1.08d Evaluate definite integrals: between limits |
6. Find the value of each of the following integrals in exact, simplified form.\\
(i) $\quad \int _ { - 1 } ^ { 0 } \mathrm { e } ^ { 1 - 2 x } \mathrm {~d} x$\\
(ii) $\int _ { 2 } ^ { 4 } \frac { 3 x ^ { 2 } - 2 } { x } \mathrm {~d} x$
\hfill \mbox{\textit{OCR C3 Q6 [8]}}