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4029 u-du : Integrating Composite Functions

4029 u-du : Integrating Composite Functions. AP Calculus. Find the derivative. dx/du-part of the antiderivative. Integrating Composite Functions (Chain Rule ) Revisit the Chain Rule If let u = inside function du = derivative of the inside becomes. u-du Substitution.

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4029 u-du : Integrating Composite Functions

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  1. 4029 u-du:Integrating Composite Functions AP Calculus

  2. Find the derivative dx/du-part of the antiderivative

  3. Integrating Composite Functions (Chain Rule) Revisit the Chain Rule If letu = inside function du = derivative of the inside becomes u-du Substitution

  4. USING u-du Substitutiona Visual Aid REM: u = inside function du = derivative of the inside let u = becomes now only working with f , the outside function A Visual Aid

  5. Example 1 : du given Ex 1: proof

  6. Example 2: du given Ex 2:

  7. Example 3: du given Ex 3:

  8. Example 4: du given Ex 4: Derivative only Function and derivative Both ways !

  9. Example 5: Regular Method Ex 5:

  10. Working with Constants < multiplying by one> Constant Property of Integration ILL. let u = du = and becomes = Or alternately = =

  11. Example 6 : Introduce a Constant - my method

  12. Example 7 : Introduce a Constant

  13. Example 8 : Introduce a Constant << triple chain>>

  14. You is what You is inside Example 9 : Introduce a Constant - extra constant << extra constant>

  15. Example 10: Polynomial

  16. Example 11: Separate the numerator

  17. Formal Change of Variables << the Extra “x”>> ILL: Let Solve for x in terms of u then and becomes

  18. Formal Change of Variables << the Extra “x”>> Rewrite in terms of u - du

  19. Assignment Day 1 Worksheet Larson HW 4029 Day 2 Basic Integration Rules Wksht extra x Larson 4029 58f anti for tan /cot Text p. 338 # 18 - 52 (3x)

  20. Integrating Composite Functions (Chain Rule) Remember: Derivatives Rules Remember: Layman’s Description of Antiderivatives *2nd meaning of “du” du is the derivative of an implicit “u”

  21. Development must have the derivative of the inside in order to find the antiderivative of the outside *2nd meaning of “dx” dx is the derivative of an implicit “x” more later if x = f then dx = f /

  22. Development from the layman’s idea of antiderivative “The Family of functions that has the given derivative” must have the derivative of the inside in order to find ---------- the antiderivative of the outside

  23. Working With Constants: Constant Property of Integration With u-du Substitution REM: u = inside function du = derivative of the inside Missing Constant? u = du = Worksheet - Part 1

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