A-Level Mathematics Revision — Integration
Revise Integration for A-Level Mathematics with a topic explanation, worked example and common mistakes. Check the board notes for specification differences.
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What 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 examples
Worked 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
Start with low-focus cards for Integration, then move into full exam-style practice when you want the heavier session.
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
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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.