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, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP.
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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.
Mini lesson for Integration
1. Understand the core idea
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.
Can you explain Integration without copying the notes?
2. Turn it into marks
Find the definite integral of x² from x=1 to x=3. The integral of x² is (1/3)x³.
Underline the method, evidence, or command-word move that would earn credit in A-Level Pure Mathematics.
3. Fix the likely mark leak
Watch for this mistake: Forgetting 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.
Write one correction rule before doing another practice question.
Practise this topic
Jump into adaptive, exam-style questions for Integration. Free to start; sign in to save progress.
Integration practice questions
These are original StudyVector questions for revision practice. They are not official exam-board questions.
Question 1
In one A-Level sentence, explain what Integration is testing.
Answer: 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...
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Integration question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Forgetting 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." What should their next repair task be?
Answer: Do one Integration question and review the mistake type.
Mark focus: Error correction and next-step practice.
Integration flashcards
Core idea
What is the main idea in 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 expo...
Common mistake
What mistake should you avoid in Integration?
Forgetting 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.
Practice
What is one useful practice task for Integration?
Answer one Integration question and review the mistake type.
Exam board
How should you use board notes for Integration?
All A-Level Maths boards (AQA, Edexcel, OCR) cover integration in depth. The complexity of the integrals and the specific techniques required (e.
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, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP specifications.
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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.