# Integration

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• Created by: eleanor
• Created on: 12-04-15 14:23
• 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
• integration by parts
• volume of revolution
• differential equations