4_5_substitution_examples - 4.5 Integration by Substitution Examples Integration by Substitution Not division by monomial Cannot easily simplify Can

4_5_substitution_examples - 4.5 Integration by Substitution...

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Unformatted text preview: 4.5 Integration by Substitution: Examples Integration by Substitution Not division by monomial. Cannot easily simplify....... Can this problem be converted to one that fits the power rule? Let 3 is not a factor of the integrand: Must complete the du, using the multiplication property of 1. Multiply by 3 3 Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: Integration by Substitution (1 of 12) 4.5 Integration by Substitution: Examples Check: Derivative of the answer should be the original integrand. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: Example 1 (2 of 12) 4.5 Integration by Substitution: Examples Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: Example 2 (3 of 12) 4.5 Integration by Substitution: Examples Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example 3 (4 of 12) 4.5 Integration by Substitution: Examples Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example 4 (5 of 12) 4.5 Integration by Substitution: Examples Some problems do not require substitution. Title: example 5 (6 of 12) 4.5 Integration by Substitution: Examples Or: find y Given the differential equation, we use the definition of the differential, dy. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example 6 (7 of 12) 4.5 Integration by Substitution: Examples Sometimes the first choice for u does not work. Try another, different choice. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example 7 (8 of 12) 4.5 Integration by Substitution: Examples Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example 8 (9 of 12) 4.5 Integration by Substitution: Examples Sometimes the given integrand is simply not integrable by the methods we know so far. Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example 9 (10 of 12) 4.5 Integration by Substitution: Examples Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example 10 (11 of 12) 4.5 Integration by Substitution: Examples Class Notes: Prof. G. Battaly, Westchester Community College, NY Calculus Home Page Homework Part 1 Homework Part 2 Title: example 11 (12 of 12) ...
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