| 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 only the standard result that ∫(1/x)dx = ln|x| and basic logarithm laws (ln 8 - ln 2 = ln(8/2) = ln 4, then 3ln 4 = ln 64). It's slightly easier than average as it's purely procedural with no problem-solving element, though the logarithm manipulation adds minimal challenge beyond the most basic questions. |
| Spec | 1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)1.08d Evaluate definite integrals: between limits |
Show that $\int_2^8 \frac{3}{x} \, dx = \ln 64$. [4]
\hfill \mbox{\textit{OCR C3 Q1 [4]}}