Moderate -0.8 This is a straightforward application of the standard integral ∫(1/x)dx = ln|x|. Students need only recognize the form, integrate to get 2ln|x|, then evaluate at the limits: 2ln(√6) - 2ln(√2) = ln6 - ln2 = ln3. It's simpler than average C3 questions as it requires just one standard technique with no algebraic manipulation or problem-solving insight.
Either or both may be implied, e.g. \(2\ln\sqrt{6} = \ln 6\) or \(\ln 6 - \ln 2 = \ln 3\)
Obtain \(\ln 3\)
A1
AG; with at least one property shown explicitly
# Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| State $2\ln x$ | B1 | May be implied by immediate use of limits |
| Use both relevant logarithm properties correctly | M1 | Either or both may be implied, e.g. $2\ln\sqrt{6} = \ln 6$ or $\ln 6 - \ln 2 = \ln 3$ |
| Obtain $\ln 3$ | A1 | AG; with at least one property shown explicitly |
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