plumiImproper integrals: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on E.2 Improper integrals, 2019–2025, 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 5 questions on Improper integrals, as a list
- June 2025, Paper 2, Q15 (6 marks): Prove that ( )( ) d 5 1 13 ln 1 2 3 12 x x x ∞ = + + ∫ Show the limiting process clearly. [6 marks]
- June 2023, Paper 2, Q14 (10 marks): The function f is defined by f (x) = 1 4x2 + 16x + 19 (x 2 R) 14 (a) Show, without using calculus, that the graph of y = f (x) has a stationary point at −2, 1 3
- November 2021, Paper 1, Q10 (6 marks): Evaluate the improper integral ( 8 0 ln x dx showing the limiting process. [6 marks]
- November 2020, Paper 1, Q1 (1 mark): Which of the integrals below is not an improper integral? Circle your answer. [1 mark] ( 1 0 e−x dx ( 2 0 1 1 − x2 dx ( 1 0 x p dx ( 1 0 1x p dx
- June 2019, Paper 2, Q13 (10 marks): (a) Explain why (1 3 x2e−2x dx is an improper integral. [1 mark] 13 (b) Evaluate (1 3 x2e−2x dx Show the limiting process. [9 marks]
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