# Integration – reversing differentiation & finding areas

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## Integration

**Integration** (which, like differentiation, is part of calculus) is the process we use to reverse differentiation and/or find areas beneath curves. Recall that, during GCSE Maths, we saw how to find the area beneath some straight line graphs (area under velocity-time graph). At A-Level, we learn how to do this for curves.

**Indefinite** and **Definite Integration** of basic polynomial functions, as well as the fundamental theorem of calculus, are taught in the first year of A-Level Maths. In the second year, we will learn multiple methods to integrate more complicated functions as listed below. We also learn how to solve differential equations.

## Other Areas in AS-Maths

- PROOF – proof by deduction, proof by exhaustion, disproof by counterexample
- ALGEBRA & FUNCTIONS – completing the square, cubics, curve sketching, discriminant, indices, inequalities, polynomials, quadratics, simultaneous equations, surds, transformations
- COORDINATE GEOMETRY – straight lines, equation of a circle
- SEQUENCES & SERIES – binomial expansion
- TRIGONOMETRY – non-right-angled triangles, trigonometric equations, trigonometric graphs, trigonometric identities
- EXPONENTIALS & LOGS – exponential & logarithmic graphs, logs, their rules and solving log equations, growth & decay, differentiating e to the kx
- DIFFERENTIATION – differentiation from first principles and differentiating polynomials, increasing & decreasing functions, stationary points, tangents & normals, differentiating e to the kx
- NUMERICAL METHODS – (not covered at AS Level)
- VECTORS – two-dimensional vectors, vector arithmetic, vectors in context

## Other Areas in A2-Maths

- PROOF – proof by contradiction
- ALGEBRA & FUNCTIONS – modulus of a function, partial fractions, inverse and composite functions, compound transformations
- COORDINATE GEOMETRY – parametric equations
- SEQUENCES & SERIES – arithmetic series (and sigma notation), geometric series, sequences, binomial expansion
- TRIGONOMETRY – radians, arc length & area of a sector, small angle approximations, reciprocal trigonometric functions, inverse trigonometric functions, double & compound angle formulae
- EXPONENTIALS & LOGARITHMS – compound transformations
- DIFFERENTIATION – concavity, convexity & inflection points, derivatives of trigonometric functions, product, quotient & chain rule, parametric & implicit differentiation, differentiating exp/log functions, differential equations & rates
- NUMERICAL METHODS – locating roots using iteration (including Newton-Raphson), trapezium rule
- VECTORS – 3D vectors