Area under a curve
What Area under a curve means in Mathematics A-Level, as defined for AQA, Pearson Edexcel, WJEC.
Definitions of Area under a curve
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Reference: WJEC
The area enclosed between a curve y = f(x), the x-axis, and the vertical boundary lines x = a and x = b, calculated using definite integration.
The definite integral of a positive function from a to b gives the area between the curve y = f(x), those limits and the x-axis.
Approximated by the sum of areas of rectangles, with regions below the x-axis contributing negatively as signed area.
If f(x) ≥ 0 on [a, b], the integral equals the area under y = f(x) between x = a and x = b.
Topics that use Area under a curve
- H: Integration (AQA A-Level)
- Integration (Pearson Edexcel A-Level)
- Integration (AS Unit 1: Pure Mathematics A) (WJEC A-Level)
Related terms
- Antiderivative
- Fundamental Theorem of Calculus
- Area between curves
- Definite integral
- definite integration
- Integration by parts
- Integration by substitution
- limits of integration
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