0606/22 May/Jun 2025, Question 8: Definite Integrals and Areas
Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 11 marks
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The question, in short
For the curve y = 15/x − 5/x², find A on the x-axis and the maximum B, then calculate the exact area between line AB and the curve.
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Solution · 11 marks
- 1A: 15/x − 5/x² = 0 gives x = 1/3
- 2dy/dx = −15/x² + 10/x³ = 0 gives x = 2/3; B is (2/3, 45/4)
- 3∫ (15/x − 5/x²) dx = 15 ln x + 5/x
- 4Area under curve from 1/3 to 2/3 = (15 ln(2/3) + 15/2) − (15 ln(1/3) + 15) = 15 ln 2 − 15/2
- 5Area of triangle under AB = (1/2) × (1/3) × 45/4 = 15/8
- 6Shaded area = 15 ln 2 − 15/2 − 15/8 = 15 ln 2 − 75/8
Answer15 ln 2 − 75/8
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Also searched as: 0606/22/M/J/25 · 0606_s25_qp_22 · 0606 s25 22 · question 8.
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