plumiIntegration by parts: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on H.7 Integration by parts, 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 7 questions on Integration by parts, as a list
- June 2025, Paper 1, Q14 (8 marks): The graph of y = 4x sin 2x for 0 ≤ x ≤ π is shown below. x y O Show that the shaded area enclosed by the x-axis and the curve is kπ, where k is an integer to be
- June 2024, Paper 3, Q11 (10 marks): The curve C with equation y = (x2 – 8x) In x is defined for x > 0 and is shown in the diagram below. The shaded region, R, lies below the x-axis and is bounded
- June 2023, Paper 1, Q8 (6 marks): Show that (p 2 0 (x sin 4x) dx = − p 8 [6 marks]
- June 2022, Paper 1, Q14 (9 marks): The region bounded by the curve y = (2x × 8) ln x and the x-axis is shaded in the diagram below. x 4 1 y 14 (a) Use the trapezium rule with 5 ordinates to find
- November 2021, Paper 3, Q8 (6 marks): Given that ( p 3 p 4 x cos x dx = ap + b find the exact value of a and the exact value of b. Fully justify your answer. [6 marks]
- June 2019, Paper 2, Q5 (7 marks): Solve the differential equation dt dx = ln x x2t for x > 0 given x = 1 when t = 2 Write your answer in the form t2 = f (x) [7 marks]
- June 2018, Paper 2, Q7 (8 marks): A function f has domain R and range fy 2 R : y × eg The graph of y = f (x) is shown. x y The gradient of the curve at the point (x, y) is given by dy dx = (x −
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