lect138_1_w11

# lect138_1_w11 - Wednesday January 5 Lecture 1: Integration...

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Wednesday January 5 Lecture 1: Integration by substitution (Refers to 5.3 and 5.5 in your text) Expectations : 1. Integrate indefinite integrals by making appropriate change of variables (substitution). 2. Integrate definite integrals by appropriate change of variables. Introduction - In calculus I we have seen that the integral of a function f ( x ), or general anti- derivative of a function f ( x ) is the family of all functions whose derivative is f ( x ). We highlight the most important results in the introduction to integration presented in Calculus I. - A theorem stating that if called if F ( x ) is a function whose derivative is f ( x ) then the family of all anti-derivatives of f ( x ) is F ( x ) + C where C is free to range over all real values was presented. - A first part of the Fundamental theorem of calculus says that, if f ( x ) is continuous on [ a , b ] and as x ranges over [ a , b ], then - The second part of Fundamental theorem of calculus says that finding the definite integral of a function f ( x ) over an interval (i.e., finding the area of the region bounded

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## lect138_1_w11 - Wednesday January 5 Lecture 1: Integration...

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