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0606/12 May/Jun 2026, Question 12: Definite Integrals and Areas

Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 11 marks

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The question, in short

Given the curve y = 10/(4x + 1) and line L through (0, 6) and (1.5, 0), find where they meet at P and Q, then calculate the exact shaded area between them.

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Solution · 11 marks

  1. 1L: y = −4x + 6
  2. 210/(4x + 1) = −4x + 6 gives 16x² − 20x + 4 = 0, i.e. 4x² − 5x + 1 = 0
  3. 3(4x − 1)(x − 1) = 0: P(1/4, 5), Q(1, 2)
  4. 4Area under L from 1/4 to 1 (trapezium) = (1/2)(5 + 2)(3/4) = 21/8
  5. 5∫ from 1/4 to 1 of 10/(4x + 1) dx = (10/4)[ln(4x + 1)] = (5/2)(ln 5 − ln 2)
  6. 6Shaded area = 21/8 − (5/2) ln(5/2)

Answer21/8 − (5/2) ln(5/2)

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