0606/12 Feb/Mar 2026, Question 11: Definite Integrals and Areas
Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 6 marks
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The question, in short
A curve is given by y = −x² + 3ax − 2a² with a positive constant a. The region between the curve and the x-axis has area 9/16; find a.
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Solution · 6 marks
- 1−x² + 3ax − 2a² = −(x − a)(x − 2a) = 0, so x = a and x = 2a
- 2Area = ∫ from a to 2a of (−x² + 3ax − 2a²) dx = 9/16
- 3[−x³/3 + 3ax²/2 − 2a²x] from a to 2a
- 4= (−8/3 + 6 − 4)a³ − (−1/3 + 3/2 − 2)a³ = a³/6
- 5a³/6 = 9/16, so a³ = 27/8
- 6a = 3/2
Answera = 3/2
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