Easy -1.2 This is a straightforward application of the standard integral ∫(1/x)dx = ln|x| + c, requiring only direct evaluation at the limits e and π. The calculation ln(π) - ln(e) = ln(π) - 1 involves minimal steps and is simpler than typical A-level integration questions that require substitution or multiple techniques.
10 In this question you must show detailed reasoning.
Show that \(\int _ { \mathrm { e } } ^ { \pi } \frac { 1 } { x } \mathrm {~d} x = \ln \pi - 1\) as given in line 37.
Convincing completion inc at least 1 intermediate line of working (AG)
[2]
## Question 10:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\int_e^{\pi} \frac{1}{x}dx = [\ln x]_e^{\pi}$ | M1 | May have $\ln\|x\|$; don't allow '$+c$' or if no [ ] or limits but condone no $dx$ |
| $\ln\pi - \ln e = \ln\pi - 1$ | A1 | Convincing completion inc at least 1 intermediate line of working (AG) |
| **[2]** | | |
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10 In this question you must show detailed reasoning.\\
Show that $\int _ { \mathrm { e } } ^ { \pi } \frac { 1 } { x } \mathrm {~d} x = \ln \pi - 1$ as given in line 37.
\hfill \mbox{\textit{OCR MEI Paper 3 2020 Q10 [2]}}