Integration as reverse differentiation
Integration as reverse differentiation
Integration reverses differentiation: if F′(x)=f(x)F'(x)=f(x)F′(x)=f(x), then ∫f(x) dx=F(x)+c\int f(x)\,dx = F(x)+c∫f(x)dx=F(x)+c. The constant +c+c+c is essential because any constant disappears when you differentiate. Later, the same idea powers area problems, differential equations and numerical estimates.
Step-by-step lessons on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one builds up to exam-style questions. Build fluency with the core pure algebra and calculus toolkit early, since almost every mechanics and statistics topic on the course depends on it.