plumiImproper integrals: Edexcel A‑Level Further Maths questions
Edexcel A-Level Further Maths past-paper questions on 5.2 Improper integrals, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 6 questions on Improper integrals, as a list
- June 2025, Core Pure 1, Q9 (9 marks): (i) The curves with equations y x = 3 4 sinh and y x tanh 1 5 intersect at just one point P (a) Use algebra to show that the x coordinate of P satisfies the equ
- June 2024, Core Pure 2, Q3 (5 marks): (a) Explain why 1 9 16 2 4 3 x x d is an improper integral. (1) (b) Show that 2 4 3 1 d 9 16 x kπ x where k is a constant to be determined. (4)
- June 2022, Core Pure 1, Q9 (6 marks): (i) (a) Explain why cosh x x 0 ∞∫ d is an improper integral. (1) (b) Show that cosh x x 0 ∞∫ d is divergent. (3) (ii) 4 sinh x = p cosh x where p is a real cons
- November 2021, Core Pure 1, Q5 (7 marks): (i) Evaluate the improper integral 2 1 1 2 e d ∞ − ∫ x x (3) (ii) The air temperature, θ °C, on a particular day in London is modelled by the equation θ = 8 – 5
- November 2020, Core Pure 1, Q2 (7 marks): (a) Explain why ( ) 1 1 d 2 5 x x x + ∫ is an improper integral. (1) (b) Prove that ( ) 1 1 d ln 2 5 x a b x x = + ∫ where a and b are rational numbers to b
- June 2019, Core Pure 1, Q2 (7 marks): Show that ( )( ) 2 0 8 12 d ln 2 3 1 x x k x x − = + + ∫ where kLVDUDWLRQDOQXPEHUWREHIRXQG (7)
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