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The area between a curve and the x-axis is found by definite integration, ∫ₐᵇ y dx. This topic covers calculating such areas, dealing with regions below the axis, and areas bounded by curves and lines. It appears across A-Level and iAL Pure Maths with the major exam boards. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
Integrate between the limits where the curve meets the x-axis or where the question tells you. If part of the region lies below the axis, that integral comes out negative, so split at the crossing point and add the sizes rather than the signed values.
Before you start
Assumed knowledge: definite integration. Examined in Pure 2. It carries straight through to area between curves and volumes of revolution. Filed under Integration.
What you learn
Integrating straight through would let the pieces cancel. The course works through signed area & regions below the axis, curves that cross the axis: total area, accumulation: area under a rate graph and mixed problem-solving. 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 Area Under a Curve as one of the Integration topics in our A-level course library, at the AS year. You work through 5 concepts and 5 worked examples, testing yourself at 5 points. Related topics students usually take next include Definite Integrals, Differential Equations, Indefinite Integrals, Integration by Parts and Integration by Substitution. For unlimited practice, the Integration revision engine builds new questions on demand and records your accuracy.
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