Integration

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  • 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
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    • 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
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    • 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
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    • volume of revolution
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    • differential equations
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