# Integration

- Created by: eleanor
- Created on: 12-04-15 14:23

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- Integration
- Reverse Chain Rule
- 1. Integrate the outside 2. divide by the inside differentiated
- only works with functions such as f(ax+b)
- f'(ax+b) = 1/a f(ax+b) + c

- Trigonometric identities
- before you integrate some trigonometric expressions you may need to replace them with functions that can be integrated
- you can't integrate sin x or cos x so you have to use the identity cos2x

- You can use partial fractions to integrate expressions by splitting them into fractions
- standard patterns
- to intergrate expressions of the form try ln |f(x)| and differentiate to check and adjust the constants
- to integrate an expression of the form kf'(x)[fx] dx try [fx]

- substitution
- 1. replace each x term with a corresponding u term. first replace dx with a term for du
- 2. rewrite the function so x is the subject
- 3. rewrite function in terms of u and simplify
- integrate and rewrite in terms of x

- 3. rewrite function in terms of u and simplify

- 2. rewrite the function so x is the subject

- 1. replace each x term with a corresponding u term. first replace dx with a term for du
- integration by parts
- volume of revolution
- differential equations

- Reverse Chain Rule

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