Leaving Cert Maths: Integration
How often Integration comes up on the Maths papers, every year it was asked, and questions to try.
HL Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
Integration, Higher Level(6 marks)
Quick ones on Integration.
(a)∫ x³ dx = ?
- 3x² + c
- x⁴/4 + c
- x⁴ + c
(b)∫ cos x dx = ?
- tan x + c
- −sin x + c
- sin x + c
(c)∫ 2x dx from 0 to 1 = ?
- 1
- ½
- 2
Show the answers
(a) x⁴/4 + c
(b) sin x + c
(c) 1
Higher Level
Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q3, Q10 |
| 2025 | Q9 |
| 2024 | Q3, Q7, Q10 |
| 2023 | Q6, Q7, Q10 |
| 2022 | Q2, Q8 |
| 2021 | Q6, Q8 |
| 2019 | Q3, Q4 |
| 2018 | Q3, Q6 |
| 2017 | Q6, Q7 |
| 2016 | Q7 |
Links open the State Examinations Commission’s paper for that year.
More Integration questions
Integration, 2 marks
∫ e²ˣ dx = ?
- 2e²ˣ + c
- e²ˣ + c
- ½e²ˣ + c
Show the answer
½e²ˣ + c
Divide by the coefficient of x in the power: ∫ eᵏˣ dx = (1/k)eᵏˣ + c. Check: d/dx (½e²ˣ) = e²ˣ.
Integration, 2 marks
∫ (2x + 1) dx = ?
- x² + c
- x² + x + c
- 2 + c
Show the answer
x² + x + c
Integrate each term: 2x → x² and 1 → x. Add c.
Integration, 2 marks
∫ (1/x) dx from 1 to e = ?
- 1
- e
- 0
Show the answer
1
∫ (1/x) dx = ln x. Evaluate: ln e − ln 1 = 1 − 0 = 1.