O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2025 · Q105 Marks
Show that ∫(from π/2 to 3π/2) ((sinθ+cosθ)² + (sinθ−cosθ)²)dθ = kπ, where k is an integer to be found.
- Show that ∫(from π/2 to 3π/2) ((sinθ+cosθ)² + (sinθ−cosθ)²)dθ = kπ, where k is an integer to be found.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [5] M1 for expansion of both terms with an attempt to simplify either using the correct identity or eliminating terms in 2sinθcosθ
- M1 Dep M1 for ∫ 2 dθ = 2θ
- Dep M1 for correct use of limits [2θ] (from π/2 to 3π/2) = 3π - π = 2π
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