plumiIntegrating exponentials, 1/x and trig functions: Edexcel A‑Level Maths questions
Edexcel A-Level Maths past-paper questions on 8.3 Integrating exponentials, 1/x and trig functions, 2010–2025, 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 8 questions on Integrating exponentials, 1/x and trig functions, as a list
- June 2025, Pure 1, Q16 (7 marks): O 1 C R x y 3 Figure 5 Figure 5 shows a sketch of the curve C with equation y = 1 4 2 2 x x − 0 < x < 2 The region R, shown shaded in Figure 5, is bounded by C,
- June 2024, Pure 1, Q7 (8 marks): Diagram not drawn to scale. L 1.5 m H m Figure 2 Figure 2 shows a cylindrical tank of height 1.5 m. Initially the tank is full of water. The water starts to lea
- June 2022, Pure 1, Q4 (3 marks): (a) Express δ 0 2.1 2 lim δ x x x x → =∑ as an integral. (1) (b) Hence show that 6.3 δ 0 2.1 2 lim δ x x x x → =∑ = ln k where k is a constant to be found. (2)
- June 2022, Pure 1, Q16 (9 marks): y 4 C R x O Figure 6 Figure 6 shows a sketch of the curve C with parametric equations x = 8 sin2 t y = 2 sin 2t + 3 sin t 0 t π 2 The region R, shown shaded
- November 2020, Pure 1, Q10 (10 marks): (a) Use the substitution x = u2 + 1 to show that 3 1 3 2 1 6 3 2 5 10 d d x x x u u u p q − ( ) + − ( ) = + ( ) ∫ ∫ where p and q are positive constants to be f
- November 2020, Pure 2, Q6 (7 marks): (a) Given that x x x Ax B C x x x 2 8 3 2 2 2 + − + ≡ + + + ∈ ≠− find the values of the constants A, B and C (3) (b) Hence, using algebraic integration, find
- June 2018, Pure 1, Q7 (7 marks): Given that k + (a) show that 2 3 3 ( ) x k x k k − ∫ d is independent of k, (4) (b) show that 2 2 2 2 ( ) x k x k k − ∫ d is inversely proportional to k. (3)
- June 2018, Pure 1, Q10 (8 marks): The height above ground, H metres, of a passenger on a roller coaster can be modelled by the differential equation d d H t H t = cos( . ) 0 25 40 where t is the
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