Curriculum Hub → Maths Lessons → Algebra → Integration → How to Teach Definite Integration | A Level Maths (Year 1 Pure)
Definite integration is the first place students apply the Fundamental Theorem of Calculus to get an actual number rather than a function plus a constant. This brief is built for planning, not revising: a quick content refresher, a video walkthrough you can watch back or set for cover, a suggested lesson sequence, and four exam questions ready to project at the end of the lesson.
The full slide deck and differentiated worksheet for this lesson — including the starter, worked examples, and practice questions referenced above — are available in the Definite Integrals lesson pack with a Mr Mathematics membership.
Want the full lesson, worksheet, and answer key ready to teach from? Grab the Definite Integrals lesson pack. View all integration lessons here.
Yes, this lesson assumes students can already integrate powers of x, including negative and fractional indices. If that’s shaky, use the starter to recap it rather than folding it into the main teaching, or the lesson will run long.
Because the constant appears in both f(a) and f(b) and cancels out when you subtract one from the other. It’s worth showing this cancellation explicitly on the board once, since it’s the question students ask most.
Forgetting to expand brackets or rewrite a fraction into separate terms before integrating, and substituting the lower limit but only subtracting part of the bracket rather than the whole evaluated expression.
Typically a single lesson, around 50 – 60 minutes, covers the method and standard evaluation questions. If you’re including “find k” problems where the limit itself is unknown, give these a larger share of the practice and plenary time” they usually need more scaffolding.
Yes, definite integration is the same content whether it sits in an AS-Level or Year 1 Pure scheme of work, so the lesson pack works for either.
Want the full lesson, worksheet, and answer key ready to teach from? Grab the Definite Integrals lesson pack.
Students learn how to evaluate a definite integral, including why the constant of integration isn't needed and how to apply correct bracket-and-limit notation.
As the lesson progresses, students extend this to finding an unknown upper or lower limit from a given integral value.
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