0606/13 May/Jun 2026, Question 11: Definite Integrals and Areas
Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 10 marks
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The question, in short
Calculate the exact area of the region bounded by the curve y = 5/(2x − 1) + 1 and the line y = 8 − 2x, using the two intersection points as limits.
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Solution · 10 marks
- 18 − 2x = 5/(2x − 1) + 1 leads to 4x² − 16x + 12 = 0
- 2(x − 1)(x − 3) = 0, x = 1, x = 3 (y = 6, y = 2)
- 3Area under line from 1 to 3 = trapezium = (1/2)(6 + 2)(2) = 8
- 4∫ (5/(2x − 1) + 1) dx = (5/2) ln(2x − 1) + x
- 5∫ from 1 to 3 of (5/(2x − 1) + 1) dx = (5/2) ln 5 + 3 − (5/2) ln 1 − 1 = 2 + (5/2) ln 5
- 6Area = 8 − (2 + (5/2) ln 5) = 6 − (5/2) ln 5
Answer6 − (5/2) ln 5
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