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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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