N2008 P1 Q5

N2008 P1 Q5

Junior College 2
7 marks
  1. Find the exact value of \(\int_0^{1/\sqrt3}\frac1{1+9x^2}\,\mathrm dx\).[3]
  2. Find, in terms of \(n\) and \(\mathrm e\), \(\int_1^{\mathrm e}x^n\ln x\,\mathrm dx\), where \(n\ne-1\).[4]

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Answer:(i) \(\pi/9\). (ii) \(\frac{n\mathrm e^{n+1}+1}{(n+1)^2}\).

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