plumiDefinite integrals and area under a curve: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on H.2 Definite integrals and area under a curve, 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 13 questions on Definite integrals and area under a curve, 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 1, Q18 (11 marks): (a) Use a suitable substitution to show that ∫ 4 0 (4x + 1)(2x + 1) 1 2 dx can be written as 1 2 ∫ 9 a (2u 3 2 – u 1 2)du where a is a constant to be found. [5
- June 2024, Paper 2, Q2 (1 mark): The graph of y = f (x) intersects the x-axis at (–3, 0), (0, 0) and (2, 0) as shown in the diagram below. y x A B 2 – 3 The shaded region A has an area of 189 T
- 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 2, Q2 (1 mark): It is given that (6 0 f (x)dx = 20 and (6 3 f (x) dx = −10 Find the value of (3 0 f (x)dx Circle your answer. [1 mark] −30 −10 10 30
- 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 1, Q15 (10 marks): (a) Show that sin x − sinx cos 2x ≤ 2x3 for small values of x. [3 marks] 15 (b) Hence, show that the area between the graph with equation y = 8( sinx − sin x co
- November 2020, Paper 3, Q1 (1 mark): Given that (10 0 f (x)dx = 7 deduce the value of (10 0 f (x) + 1 dx Circle your answer. [1 mark] −3 7 8 17
- June 2019, Paper 1, Q14 (10 marks): The graph of y = 2x3 x2 + 1 is shown for 0 ≤ x ≤ 4 4 x 0 0 2 4 6 8 y 2 A Caroline is attempting to approximate the shaded area, A, under the curve using the tra
- June 2019, Paper 1, Q16 (16 marks): (a) y = e−x( sinx + cos x) Find dy dx Simplify your answer. [3 marks] 16 (b) Hence, show that ( e−x sinx dx = ae−x( sinx + cos x) + c where a is a rational numb
- June 2019, Paper 2, Q9 (9 marks): (a) Show that the first two terms of the binomial expansion of 4 − 2x2 p are 2 − x2 2 [2 marks] 9 (b) State the range of values of x for which the expansion fou
- June 2018, Paper 1, Q6 (12 marks): (a) Find the first three terms, in ascending powers of x, of the binomial expansion of 1 4 + x p [3 marks] 6 (b) Hence, find the first three terms of the binomi
- June 2018, Paper 2, Q3 (1 mark): The graph of y = x3 is shown. x 1 0 y 2 –1 –2 –3 3 4 Find the total shaded area. Circle your answer. [1 mark] −68 60 68 128
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