2024 IGCSE Additional Mathematics May/June 0606/12 Q11

2024 IGCSE Additional Mathematics May/June 0606/12 Q11

5 marks
  1. Given that \(y=x^2\ln x\), find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\).[2]
  2. Hence find \(\displaystyle\int x\ln x\,\mathrm{d}x\).[3]

Solution:

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Answer:(a) \(x+2x\ln x\). (b) \(\dfrac12x^2\ln x-\dfrac14x^2+C\).

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