CRMS Calculus 2010 March 31, 2010
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Transcript of CRMS Calculus 2010 March 31, 2010
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Derivative Integral
Section 5.3A: Integration and the Indefinite Integral
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(Variable of integration: " with respect to x ".)
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" undo " each other.
Differentiation and Integration are ____________________ operations.
( )
Differentiate ( verb )
To find the instantaneousrate of change of function
Integrate ( verb )
To find the family of functionswhose derivative
is function
( )
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III. Mechanics. The rules of integration mirror the rules of differentiation.
Differentiation Integration
1. Power Rule 1. Power Rule
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2. Constant Rule 2. Constant Rule (Power Rule Special case for x 0 )
Differentiation Integration
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3. Constant times a function 3. Constant times a function
Differentiation Integration
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Differentiation Integration
4. Sum of Functions 4. Sum of Functions
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Differentiation Integration
5. Natural Exponential Function 5. Natural Exponential Function
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Differentiation Integration
6. Base b Exponential Functions 6. Base b Exponential Functions
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Differentiation Integration
("u" Substitution)(the Chain Rule)7. Composite Functions 7. Composite Functions
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