4029 udu Integrating Composite Functions AP Calculus Find
- Slides: 25
4029 u-du: Integrating Composite Functions AP Calculus
Find the derivative dx/du-part of the antiderivative
u-du Substitution Integrating Composite Functions (Chain Rule) Revisit the Chain Rule If let u = inside function du = derivative of the inside becomes
A Visual Aid 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
Example 1 : Ex du given 1: f o o r p
Example 2: du given Ex 2:
Example 3: du given Ex 3:
Example 4: du given Ex 4: Derivative only Function and derivative Both ways !
Example 5: Regular Method Ex 5:
Working with Constants < multiplying by one> Constant Property of Integration ILL. let u = du = and becomes = Or alternately =
Example 6 : Introduce a Constant - my method
Example 7 : Introduce a Constant
Example 8 : Introduce a Constant << triple chain>>
Example 9 : Introduce a Constant - extra constant You is what You is inside << extra constant>
Example 10 : Polynomial
Example 11: Separate the numerator
Formal Change of Variables << the Extra “x”>> ILL: Let Solve for x in terms of u then and becomes
Formal Change of Variables << the Extra “x”>> Rewrite in terms of u - du
Assignment Day 1 Worksheet Larson HW 4029 Day 2 Basic Integration Rules Wksht extra x Larson 4029 58 f anti for tan /cot Text p. 338 # 18 - 52 (3 x)
Integrating Composite Functions (Chain Rule) Remember: Derivatives Rules Remember: Layman’s Description of Antiderivatives *2 nd meaning of “du” du is the derivative of an implicit “u”
Development must have the derivative of the inside in order to find the antiderivative of the outside *2 nd meaning of “dx” dx is the derivative of an implicit “x” if x = f then dx = f / more later
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
Working With Constants: Constant Property of Integration With u-du Substitution REM: u = inside function du = derivative of the inside Missing Constant? Worksheet - Part 1 u = du =
