Integration Techniques

Here are the integration formulae and techniques tested for H2 A Level Math exam.

General Properties of Integration

1. 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

Note: There are NO product rule, chain rule or quotient rule for integration.

Integration Formulae

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
• f(x)
• dx

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.

Videos on Integration – H2 A Level Math

• Watch a summary of the integration formula here.

• Watch some important concepts about integration here.

H2 A Level Math Notes

• You can find the compilation of H2 A Level Math Notes here.