Integration — A-Level Mathematics Revision
Revise Integration for A-Level Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
At a glance
- What StudyVector is
- An exam-practice platform with board-aligned questions, explanations, and adaptive next steps.
- This topic
- Integration in A-Level Mathematics: explanation, examples, and practice links on this page.
- Who it’s for
- Students revising A-Level Mathematics for UK exams.
- Exam boards
- Practice is aligned to major specifications (AQA, Edexcel, OCR, WJEC, Eduqas, Cambridge International (CIE), SQA, IB, AP).
- Free plan
- Sign up free to use tutor paths and full feedback on your answers. Pricing
- What makes it different
- Syllabus-shaped practice and progress tracking—not generic AI answers.
Topic has curated content entry with explanation, mistakes, and worked example. [auto-gate:promote; score=75.25]
Next in this topic area
Next step: Numerical Methods
Continue in the same course — structured practice and explanations on StudyVector.
Go to Numerical MethodsWhat is Integration?
Integration at A-Level is the reverse process of differentiation and is used to find the area under a curve. You will learn to integrate a variety of functions, including polynomials, trigonometric functions, and exponentials, and use techniques like integration by substitution and integration by parts.
Board notes: All A-Level Maths boards (AQA, Edexcel, OCR) cover integration in depth. The complexity of the integrals and the specific techniques required (e.g., integration by parts) can vary slightly between boards.
Step-by-step explanationWorked example
Find the definite integral of x² from x=1 to x=3. The integral of x² is (1/3)x³. Evaluating this between 1 and 3 gives [(1/3)(3)³] - [(1/3)(1)³] = (27/3) - (1/3) = 26/3.
Practise this topic
Jump into adaptive, exam-style questions for Integration. Free to start; sign in to save progress.
Common mistakes
- 1Forgetting to add the constant of integration, 'C', when finding an indefinite integral. This is a crucial step as the derivative of a constant is zero.
- 2Making errors with the limits of integration when evaluating a definite integral. The lower limit must be subtracted from the upper limit.
- 3Confusing integration by substitution and integration by parts. It's important to recognise which technique is appropriate for a given integral.
Integration exam questions
Exam-style questions for Integration with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
Integration exam questionsGet help with Integration
Get a personalised explanation for Integration from the StudyVector tutor. Ask follow-up questions and work through problems with step-by-step support.
Open tutorFree full access to Integration
Sign up in 30 seconds to unlock step-by-step explanations, exam-style practice, instant feedback and on-demand coaching — completely free, no card required.
Try a practice question
Unlock Integration practice questions
Get instant feedback, step-by-step help and exam-style practice — free, no card needed.
Start Free — No Card NeededAlready have an account? Log in
Step-by-step method
Step-by-step explanation
4 steps · Worked method for Integration
Core concept
Integration at A-Level is the reverse process of differentiation and is used to find the area under a curve. You will learn to integrate a variety of functions, including polynomials, trigonometric fu…
Frequently asked questions
What is the difference between a definite and an indefinite integral?
An indefinite integral is a function, representing the family of antiderivatives of a function. A definite integral is a number, representing the area under the curve of a function between two given limits.
How is integration used to find the area between two curves?
To find the area between two curves, you integrate the difference of the two functions over the desired interval. You need to be careful to subtract the lower curve from the upper curve.