Here are the integration formulae and techniques tested for H2 A Level Math exam.
General Properties of Integration
- Integration is the reverse of differentiation.
2. ∫k f(x) dx = k∫f(x) dx + c, where k is a constant
3. ∫[f(x) ± g(x)] dx = ∫f(x) dx ±∫g(x) dx
General Formulae for Integration
Integration of Algebraic Functions
Integration of Trigonometric Functions
Integration by Substitution
When integrating a function by substitution, we replace one variable by another variable. When doing an integration by substitution, make sure you substitute these 3 items with the other variable:
- Limits (i.e. a and b) – for definite integration only
Integration by Parts
When doing integration by parts, we split the function to be integrated into 2 parts, and let one part be u and the other part be dv/dx.
Then, we do the integration by parts using the formula:
The order of choice for u is Logarithm, Inverse Trigonometry, Algebraic, Trigonometry, Exponential. This is commonly known as LIATE.