Integration – reversing differentiation & finding areas
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