Integration by Substitution

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Presentation transcript:

Integration by Substitution AP Calculus March 27-28, 2017 Mrs. Agnew

Essential Question Essential Vocabulary How do you evaluate integrals using substitution? Essential Vocabulary Integration by Substitution Definite Integral Indefinite Integral

Integration by Substitution So far, we have evaluated only those integrals where we could find an antiderivative using our rules. Evaluate the following… what is the problem?

Integration by Substitution Given a composite function (a “function within a function”), the antiderivative is given by… Integration by substitution “undoes” the chain rule for differentiation.

Integration by Substitution We will be making the following substitutions u = g(x) and du = g'(x) So rewriting the previous formula…

Integration by Substitution Find the “inside” function and its derivative. Replace the “inside” function with u and its derivative with du. Find the antiderivative. Replace u with the function and simplify. CHAIN RULE IN REVERSE! Practice: Page 395 #2 – 29 (Every 3rd)

Definite Integrals When using integration by substitution with definite integrals, you must adjust the limits of integration. a and b are the original limits of integration u = g(x)

Practice and Homework Guided Practice Homework Page 395 #38 – 44 (E), 50, 56 Homework See Worksheet Provided Homework may be collected for grade