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This topic finds the area enclosed between two curves, or a curve and a line, by integrating the difference of the two functions between their points of intersection. 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
Find where the curves meet by solving them simultaneously — those are your limits. Integrate the upper curve minus the lower curve between them. Sketching first tells you which is which, and stops the answer coming out negative.
Before you start
Best tackled after area under a curve and solving simultaneously. It carries straight through to harder area problems.
What you learn
If two graphs meet at three points, they enclose two regions, and the upper graph swaps at the middle crossing. Both forms give the same answer; use whichever keeps the algebra tidy. Some regions are bounded by a curve and two straight lines (or an axis). The course works through curve meets curve, when the graphs cross inside: split & sum, the subtract-areas method, regions with three boundaries and harder & exact regions. 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
In our A-level maths courses, Area Between Two Curves belongs to Integration and is met in the AS year. There are 5 teaching sections and 5 fully worked examples, plus 5 sets of check questions. Students often pair it with Area Under a Curve, Definite Integrals and Differential Equations. Endless extra practice on this strand is available on the Integration revision engine, which generates a fresh question each time.
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