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An indefinite integral reverses differentiation and includes an arbitrary constant, +c. This topic covers integrating xⁿ and sums of terms and finding the particular function when a point is known. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
Integrate term by term, raising each power and dividing by the new one, and add a single constant of integration at the end. If the question gives a point on the curve, substitute it to find the value of that constant.
Before you start
Everything here rests on integration of powers. This sits in Pure 1. It carries straight through to definite integrals and areas. It is part of the Integration strand.
What you learn
This lesson covers the notation, and how to recover a curve from its gradient. Integration recovers a quantity from its rate of change. The course works through finding a curve from its gradient, boundary conditions with indices & surds and modelling with an initial condition. 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
Indefinite Integrals is a Integration topic in the A-level syllabus, covered here at the AS year. There are 5 teaching sections and 5 fully worked examples, plus 5 sets of check questions. Related topics students usually take next include Integration by Parts, Integration by Substitution, Integration of f(ax+b), Integration of Standard Functions and Integration of Trig Functions. You can drill this strand further on the Integration revision engine, with your accuracy saved to your skill tree.
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