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**Unformatted text preview: **4.5 Integration by Substitution HW: p. 304 # 19, 13, 21, 2529, 35, 37 4557, 63, 65 Class Notes: Prof. G. Battaly, Westchester Community College, NY
Calculus Home Page Homework Part 1 Homework Part 2 Title: Substitution Concept (1 of 10) 4.5 Integration by Substitution Remember the Chain Rule Complete the table. Class Notes: Prof. G. Battaly, Westchester Community College, NY
Calculus Home Page Homework Part 1 Homework Part 2 Title: Substitution Concept (2 of 10) 4.5 Integration by Substitution 1. All derivatives here use the Chain Rule to find the derivative of composite functions. Class Notes: Prof. G. Battaly, Westchester Community College, NY
Calculus Home Page Homework Part 1 Homework Part 2 Title: Chain Rule (3 of 10) 4.5 Integration by Substitution Derivative of the primary function. Derivative of the nested function. 2. To find the integrals of functions that are the derivatives of composite functions, the integrand requires the presence of the derivative of the nested function as a factor. his is the reverse T process of the Chain Rule.
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Calculus Home Page Homework Part 1 Homework Part 2 Title: Integration & Composite Functions (4 of 10) 4.5 Integration by Substitution Think: 1. This integrand is the result of the chain rule. 2. How do I reverse the operation of the chain rule? The chain rule involves multiplication. 1. Look for factors of the integrand. 2. Find the factors such that one factor is the derivative of the other factor. 3. Identify the factor u. 4. Is the remaining portion of the integrand the correct du? 5. If not, can you correct it by scalar multiplication?
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Calculus Home Page Homework Part 1 Homework Part 2 Title: Substitution Example (5 of 10) 4.5 Integration by Substitution du is not complete Class Notes: Prof. G. Battaly, Westchester Community College, NY
Calculus Home Page Homework Part 1 Homework Part 2 Title: Substitution Example (6 of 10) 4.5 Integration by Substitution
Use the multiplication property of one: multiply by 3/3 Class Notes: Prof. G. Battaly, Westchester Community College, NY
Calculus Home Page Homework Part 1 Homework Part 2 Title: Substitution Example (7 of 10) 4.5 Integration by Substitution Class Notes: Prof. G. Battaly, Westchester Community College, NY
Calculus Home Page Homework Part 1 Homework Part 2 Title: Substitution Example (8 of 10) 4.5 Integration by Substitution Class Notes: Prof. G. Battaly, Westchester Community College, NY
Calculus Home Page Homework Part 1 Homework Part 2 Title: Substitution Example (9 of 10) 4.5 Integration by Substitution Class Notes: Prof. G. Battaly, Westchester Community College, NY
Calculus Home Page Homework Part 1 Homework Part 2 Title: Homework (10 of 10) ...

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