2024 IGCSE Additional Mathematics October/November 0606/21 Q2

2024 IGCSE Additional Mathematics October/November 0606/21 Q2

4 marks
  1. Given that \(y=\tan x-x\), find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\). Write your answer in terms of \(\tan x\).[2]
  2. Hence find \(\displaystyle\int_0^{\frac\pi4}\tan^2x\,\mathrm{d}x\). Give your answer in exact form.[2]

Solution:

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Answer:(a) \(\tan^2x\). (b) \(1-\dfrac\pi4\).

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