plumiIntegration by substitution: WJEC A‑Level Maths questions
WJEC A-Level Maths past-paper questions on 8.5 Integration by substitution, 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 5 questions on Integration by substitution, as a list
- Summer 2025, Unit 3, Q14 (11 marks): 2 x cos d x x 14. (a) Use integration by parts to find the exact value of . [6] 0 ln x d x u 1 ln x . (b) Use the substitution to find [5] 2 x 1 ln
- Summer 2023, Unit 3, Q14 (8 marks): 1∫ ( ) e2xdx . 3x −1 1 4 a) Use integration by parts to evaluate [4] 0 sin x d u 1 2cos x x b) Use the substitution to find . [4] 1 2cos x
- Summer 2022, Unit 3, Q18 (7 marks): 8 a) Use a suitable substitution to find ∫ x2 dx . [5] ( )4 x + 3 1∫ x2 b) Hence evaluate . dx [2] ( )4 x + 3 0
- Summer 2019, Unit 3, Q14 (11 marks): ∫ Find (e2x + 6sin3x) dx. 1 4 a) [2] ∫ Find 7(x2 + sinx)6(2x + cosx) dx. b) [1] ∫ 1 c) Find . lnxdx [4] x2 Use the substitution u = 2cosx + 1 to evaluate d) π 3
- Summer 2018, Unit 3, Q14 (12 marks): 4 Evaluate 2∫ x3 ln x dx a) . [6] 1 2 + x 1∫ dx b) . [6] 4 − x2 0
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