0606/13 Oct/Nov 2025, Question 8: Definite Integrals and Areas
Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 7 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Two curves, y = 12 − x² and y = x⁴ − 4x² + 8, cross at two points; calculate the area trapped between them.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 7 marks
- 112 − x² = x⁴ − 4x² + 8 gives −x⁴ + 3x² + 4 = 0
- 2(x² − 4)(x² + 1) = 0, so x = 2 and x = −2 only
- 3Area = ∫ from −2 to 2 of (−x⁴ + 3x² + 4) dx
- 4= [−x⁵/5 + x³ + 4x] from −2 to 2
- 5= (−32/5 + 8 + 8) − (32/5 − 8 − 8)
- 6= 96/5 = 19.2
Answer96/5 or 19.2
Stuck on a step? Read the free lesson: Definite Integrals and Areas
Practise more definite integrals and areas 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 definite integrals and areas
Also searched as: 0606/13/O/N/25 · 0606_w25_qp_13 · 0606 w25 13 · question 8.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.