# Lecture 15 & Lab 15 (Integration [Anti-Differentiation]) [Part 1](2)

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Calculus I(Lecture 15 & Lab #15)Integration [a.k.a. AntiDifferentiation] [Part 1]Ziad Z. AdwanLecture 15 & Lab 151 / 47
Topics Covered in this Lecture:Topic 1Antiderivatives & Indefinite IntegrationTopic 2Integration by SubstitutionZiad Z. AdwanLecture 15 & Lab 152 / 47
Topic 1 & its Learning Objectives:Topic 1Antiderivatives & Indefinite IntegrationAntiderivatives [De°nition & Notation].Solving Di/erential Equations.Integration as an Inverse Process to Di/erentiation.7 Basic Rules for Integration.Examples & Lab Problems on the 7 Basic Rules for Integration.Ziad Z. AdwanLecture 15 & Lab 153 / 47
Motivation for AntiderivativesSuppose that you are asked to °nd a functionFwhose derivative isf(x) =4x3.Ziad Z. AdwanLecture 15 & Lab 154 / 47
Motivation for AntiderivativesSuppose that you are asked to °nd a functionFwhose derivative isf(x) =4x3.From your knowledge of Derivatives, you would probably say thatF(x) =x4becauseddx°x4±=4x3.Such a functionFis called anAntiderivativeoff.Ziad Z. AdwanLecture 15 & Lab 154 / 47
Motivation for AntiderivativesSuppose that you are asked to °nd a functionFwhose derivative isf(x) =4x3.From your knowledge of Derivatives, you would probably say thatF(x) =x4becauseddx°x4±=4x3.Such a functionFis called anAntiderivativeoff.Suppose now that you are asked to °ndALLfunctionsFwhose derivative isf(x) =4x3. IsF(x) =x4the ONLY such function?
Lecture 15 & Lab 154 / 47
Motivation for AntiderivativesSuppose that you are asked to °nd a functionFwhose derivative isf(x) =4x3.From your knowledge of Derivatives, you would probably say thatF(x) =x4becauseddx°x4±=4x3.Such a functionFis called anAntiderivativeoff.Suppose now that you are asked to °ndALLfunctionsFwhose derivative isf(x) =4x3. IsF(x) =x4the ONLY such function?
Lecture 15 & Lab 154 / 47
Motivation for AntiderivativesSuppose that you are asked to °nd a functionFwhose derivative isf(x) =4x3.From your knowledge of Derivatives, you would probably say thatF(x) =x4becauseddx°x4±=4x3.Such a functionFis called anAntiderivativeoff.Suppose now that you are asked to °ndALLfunctionsFwhose derivative isf(x) =4x3. IsF(x) =x4the ONLY such function?