0606/11 May/Jun 2026, Question 10: Integrating eˣ, Trig and (ax+b)ⁿ
Cambridge IGCSE Additional Mathematics 0606 · Paper 11 (Non-calculator) · Non-calculator · 8 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Given the second derivative (2x + 10)^(−1/2) − 2x and a stationary point at (3, 64/3), determine the curve's equation y = f(x).
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 8 marks
- 1f′(x) = (2x + 10)^(1/2) − x² + c
- 2Stationary at x = 3: √16 − 9 + c = 0, so c = 5
- 3f(x) = (1/3)(2x + 10)^(3/2) − x³/3 + 5x + d
- 4At (3, 64/3): (1/3)(64) − 9 + 15 + d = 64/3
- 5d = −6
- 6y = (1/3)(2x + 10)^(3/2) − x³/3 + 5x − 6
Answery = (1/3)(2x + 10)^(3/2) − x³/3 + 5x − 6
Stuck on a step? Read the free lesson: Integrating eˣ, Trig and (ax+b)ⁿ
Practise more integrating eˣ, trig and (ax+b)ⁿ questions
Real 0606 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on integrating eˣ, trig and (ax+b)ⁿ
Also searched as: 0606/11/M/J/26 · 0606_s26_qp_11 · 0606 s26 11 · question 10.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.