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A definite integral evaluates accumulated change between two limits to give a numerical answer. This topic covers evaluating ∫ₐᵇ f(x) dx using the limits and applying it to find areas. It appears across A-Level and iAL Pure Maths with the major exam boards. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
Integrate as usual, then substitute the upper limit and subtract the value at the lower limit. Write the integrated function in square brackets with the limits before substituting. No constant of integration is needed because it cancels.
Before you start
Bring indefinite integration with you. It belongs to the Pure 2 specification. It reappears throughout area under a curve and between curves.
What you learn
And substitute carefully with negative limits. Definite integrals of surds work the same way — rewrite as powers first. This works while the curve stays above the axis. The course works through evaluating a definite integral, surds & key properties, area under a curve, area between two graphs and points of intersection as limits. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
We teach Definite Integrals as one of the Integration topics in our A-level course library, at the AS year. The course is built from 5 concept sections, 5 worked examples and 5 check points before the exam-style set. Students often pair it with Differential Equations, Indefinite Integrals, Integration by Parts and Integration by Substitution. The Integration revision engine gives you as many extra questions as you want, tracked on your skill tree.
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