2025 IGCSE Additional Mathematics October/November 0606/23 Q4

2025 IGCSE Additional Mathematics October/November 0606/23 Q4

7 marks
  1. Integrate the following with respect to \(x\).
    1. \(\mathrm e^{5x-2}\)[2]
    2. \(\dfrac1{4-3x}\) where \(x<\dfrac43\)[2]
  2. Show that \(\displaystyle\int_{\pi/3}^{\pi/2}\sec^2(\tfrac12x)\,\mathrm dx=2\left(1-\dfrac{\sqrt3}3\right)\).[3]

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Answer:(a)(i) \(\tfrac15\mathrm e^{5x-2}+C\) (ii) \(-\tfrac13\ln(4-3x)+C\) (b) Shown.

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