A Level Maths: Integration Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
- Definite and Indefinite Integrals (OCR)
- Definite and Indefinite Integrals (Edexcel)
- Finding the Equation of a Curve Given the Differential (OCR)
- Finding the Equation of a Curve Given the Differential (Edexcel)
- Area Between a Curve and the x-Axis (OCR)
- Area Between a Curve and the x-Axis (Edexcel)
- Integration Mixed (OCR)
- Mixed Calculus (OCR)
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Differentiation — integration is its reverse, so fluency with differentiation is essential
- Indices — needed for rewriting expressions before integrating
- Quadratic Equations — needed for finding limits and intersection points
A Level Maths integration is the second half of calculus, the reverse process of Differentiation. Given a derivative, integration recovers the original function (up to a constant). Given a curve, integration finds the area underneath it. These two pictures — antiderivative and area — are linked by the fundamental theorem of calculus, one of the most important results in mathematics.
At Year 1 you integrate any power of $x$ (except $x^{-1}$) using the reverse power rule: $\int x^n \, dx = \frac{x^{n+1}}{n+1} + c$, including for negative and fractional indices. You handle indefinite integrals (with the $+c$ constant of integration) and definite integrals (which evaluate to a number representing the area under a curve between two limits). You find the area between a curve and the $x$-axis, handling cases where the curve dips below the axis by treating regions separately. Given a derivative and a point on the original curve, you find the equation of the curve. You also solve simple first-order differential equations by integrating both sides.
Integration is part of the Pure Maths strand of A Level Maths and is essential revision content for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: NEVER forget the $+c$ on indefinite integrals; the reverse power rule does NOT work for $x^{-1}$, which integrates to $\ln|x| + c$ (covered in Further Integration); when finding area, regions below the $x$-axis give negative integrals — for total area you may need to split the integral and take absolute values; and when finding a curve from its derivative, you need an initial condition (a point on the curve) to determine the constant of integration.