Section 5.3A:   Integration and the Indefinite Integral




                      Derivative              Integral




   ...
2
3
(Variable of integration: "   with respect to x   ".)




                                                        4
Differentiate (         verb )                                                               Integrate (     verb )

     ...
III. Mechanics.       The rules of integration mirror the rules of differentiation.

Differentiation                      ...
Differentiation        Integration
2.  Constant Rule    2.  Constant Rule 
                                               ...
Differentiation                  Integration
3.  Constant times a function   3.  Constant times a function




           ...
Differentiation       Integration
4.  Sum of Functions   4.  Sum of Functions




                                        ...
Differentiation                   Integration
5.  Natural Exponential Function   5.  Natural Exponential Function




    ...
Differentiation                    Integration
6.  Base­ b Exponential Functions   6.  Base­ b Exponential Functions




 ...
Differentiation          Integration

7.  Composite Functions   7.  Composite Functions
    (the Chain Rule)          ("u"...
13
14
15
16
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CRMS Calculus 2010 March 31, 2010

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Section 5.3, Day 1: Integration rules

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CRMS Calculus 2010 March 31, 2010

  1. 1. Section 5.3A:   Integration and the Indefinite Integral Derivative Integral 1
  2. 2. 2
  3. 3. 3
  4. 4. (Variable of integration: " with respect to x ".) 4
  5. 5. Differentiate ( verb ) Integrate ( verb ) ( ) ( ) To find the instantaneous To find the family of functions rate of change  whose derivative of function is function Differentiation and Integration are  ____________________  operations.  " undo "            each other. 5
  6. 6. III. Mechanics.       The rules of integration mirror the rules of differentiation. Differentiation Integration 1.  Power Rule 1.  Power Rule 6
  7. 7. Differentiation Integration 2.  Constant Rule  2.  Constant Rule  0 (Power Rule Special case for x ) 7
  8. 8. Differentiation Integration 3.  Constant times a function 3.  Constant times a function 8
  9. 9. Differentiation Integration 4.  Sum of Functions 4.  Sum of Functions 9
  10. 10. Differentiation Integration 5.  Natural Exponential Function 5.  Natural Exponential Function 10
  11. 11. Differentiation Integration 6.  Base­ b Exponential Functions 6.  Base­ b Exponential Functions 11
  12. 12. Differentiation Integration 7.  Composite Functions 7.  Composite Functions (the Chain Rule) ("u" Substitution) 12
  13. 13. 13
  14. 14. 14
  15. 15. 15
  16. 16. 16

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