plumiDefinite integrals and area under a curve: OCR MEI A‑Level Maths questions
OCR MEI A-Level Maths past-paper questions on 8.2 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 2, Q14 (15 marks): 3 14 The equation of a curve is y + x . = 2 x (a) Determine the coordinates of the point where the curve cuts the x-axis. [2] d . y (b) (i) Find x [2] d 16 3 (i
- June 2025, AS Paper 2, Q13 (6 marks): In this question you must show detailed reasoning Determine the exact value of c 6 2 d m 8 y x , + 3 2 )x x ( 1 giving your answer in its simplest form. [6]
- June 2024, Paper 1, Q8 (6 marks): The equation of a curve is y sin 4 x 2 cos 2 x , where x is in radians. = + 4 2 (a) Show that, for small values of x, y 2 x 2 x . [2] . + - The diagram shows th
- June 2024, Paper 3, Q3 (4 marks): In this question you must show detailed reasoning. x5 The diagram shows the curve with equation y and the square OABC where the points A, B = and C have coordin
- June 2024, AS Paper 2, Q11 (6 marks): In this question you must show detailed reasoning. The equation of a curve is y 5 x - - for x x 6 0 . = H (a) Verify that the curve cuts the x-axis at x 4 and a
- June 2023, AS Paper 1, Q7 (6 marks): In this question you must show detailed reasoning. y x O Find the exact area of the shaded region shown in the diagram, enclosed by the x-axis and the 2 curve y
- June 2022, AS Paper 2, Q10 (9 marks): In this question you must show detailed reasoning. 3 2 The equation of a curve is y 12 x 24 x 60 x 72 . = - - + Determine the magnitude of the total area bounde
- November 2020, AS Paper 2, Q6 (6 marks): Use integration to show that the area bounded by the x-axis and the curve with equation 4 square units. 2 y ( x 1 ) ( x 3 ) is 3 [6] = - -
- June 2019, Paper 1, Q1 (3 marks): In this question you must show detailed reasoning. ^ h 9 y 233 Show that 2 x x d x . [3] + = 3 4
- June 2019, AS Paper 2, Q7 (8 marks): c 11 d m y 3 7 (a) Find x x x [5] 15 . + 3 x c 11 m 8 y 3 11 (b) Show that x x x a , where a is a positive integer to be determined. [3] 15 d 2 + = # 3 x 0
- June 2018, Paper 1, Q10 (8 marks): Fig. 10 shows the graph of y ( k x ) ln x where k is a constant ( k 2 1 ) . = - y x O Fig. 10 Find, in terms of k, the area of the finite region between the cur
- June 2018, AS Paper 1, Q8 (8 marks): In this question you must show detailed reasoning. Fig. 8 shows the graph of a quadratic function. The graph crosses the axes at the points (-1, 0), (0, -4) and
- June 2018, AS Paper 2, Q6 (4 marks): y 6 x x [4] Show that ( 3 4 ) d 99 . + = 0
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