| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Standard Integrals and Reverse Chain Rule |
| Type | Definite integral with logarithmic form |
| Difficulty | Moderate -0.5 This is a straightforward integration question requiring recognition of the standard form ∫(1/x)dx = ln|x| with a linear substitution. The calculation is direct: integrate to get (1/2)ln|4x-1|, evaluate at limits to get (1/2)(ln27 - ln3) = (1/2)ln9 = ln3. Slightly easier than average as it's purely procedural with no problem-solving element. |
| Spec | 1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)1.08d Evaluate definite integrals: between limits |
Show that
$$\int_1^7 \frac{2}{4x-1} \, dx = \ln 3.$$ [4]
\hfill \mbox{\textit{OCR C3 Q1 [4]}}