0606/11 Oct/Nov 2025, Question 10: Definite Integrals and Areas
Cambridge IGCSE Additional Mathematics 0606 · Paper 11 (Non-calculator) · Non-calculator · 11 marks
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The question, in short
For the curve y = x² − 9x + 18 and the normal line at x = 5, work out the area of the shaded region enclosed between them below the x-axis.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 11 marks
- 1dy/dx = 2x − 9 = 1 at x = 5; y = −2 there
- 2Normal gradient −1: y + 2 = −(x − 5) ⇒ y = −x + 3
- 3−x + 3 = x² − 9x + 18 ⇒ x² − 8x + 15 = 0 ⇒ x = 3 (or 5)
- 4Area = ∫ from 3 to 5 of [(−x + 3) − (x² − 9x + 18)] dx = ∫ from 3 to 5 of (−x² + 8x − 15) dx
- 5= [−x³/3 + 4x² − 15x] from 3 to 5
- 6= (−125/3 + 100 − 75) − (−9 + 36 − 45) = 4/3
Answer4/3
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