# 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 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.

## H2 A Level Math Notes

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