SlideShare ist ein Scribd-Unternehmen logo
1 von 11
Downloaden Sie, um offline zu lesen
Integration By Parts or




                       How to find the
                       missing piece ...




 no telling where the money went by flickr user Adam_T4
Substitution ... when some pieces are missing ...
Substitution ... when some pieces are missing ...
How do we antidifferentiate this?




                    A little algebraic massage gives ...
                          Integration by Parts




                                      Now, about that antiderivative ...
Antidifferentiate this!

                          Integration by Parts
Your turn ...   Integration by Parts
A word for the wise ...
                          Integration by Parts



                 How to decide which function will be ƒ


                          LIATE
Your turn ...   Integration by Parts




                                       LIATE
AP Calculus February 4, 2009

Weitere ähnliche Inhalte

Mehr von Darren Kuropatwa

Digital Storytelling for Deeper Learning v1
Digital Storytelling for Deeper Learning v1Digital Storytelling for Deeper Learning v1
Digital Storytelling for Deeper Learning v1Darren Kuropatwa
 
Tales of Learning and the Gifts of Footprints v4.2
Tales of Learning and the Gifts of Footprints v4.2Tales of Learning and the Gifts of Footprints v4.2
Tales of Learning and the Gifts of Footprints v4.2Darren Kuropatwa
 
Making Student Thinking Visible v4
 Making Student Thinking Visible v4 Making Student Thinking Visible v4
Making Student Thinking Visible v4Darren Kuropatwa
 
Leveraging Digital for Deeper Learning
Leveraging Digital for Deeper LearningLeveraging Digital for Deeper Learning
Leveraging Digital for Deeper LearningDarren Kuropatwa
 
We Learn Through Stories at PRIZMAH17
We Learn Through Stories at PRIZMAH17We Learn Through Stories at PRIZMAH17
We Learn Through Stories at PRIZMAH17Darren Kuropatwa
 
Providing Permission to Wonder v3
Providing Permission to Wonder v3Providing Permission to Wonder v3
Providing Permission to Wonder v3Darren Kuropatwa
 
Making Student Thinking Visible v3.7
 Making Student Thinking Visible v3.7 Making Student Thinking Visible v3.7
Making Student Thinking Visible v3.7Darren Kuropatwa
 
Providing Permission to Wonder v2
Providing Permission to Wonder v2Providing Permission to Wonder v2
Providing Permission to Wonder v2Darren Kuropatwa
 
We Learn Through Stories v4 (master class)
We Learn Through Stories v4 (master class)We Learn Through Stories v4 (master class)
We Learn Through Stories v4 (master class)Darren Kuropatwa
 
Deep Learning Design: the middle ring
Deep Learning Design: the middle ringDeep Learning Design: the middle ring
Deep Learning Design: the middle ringDarren Kuropatwa
 
HSD Digital Citizenship Framework
HSD Digital Citizenship FrameworkHSD Digital Citizenship Framework
HSD Digital Citizenship FrameworkDarren Kuropatwa
 
Albertville Elementary School: Learning Together
Albertville Elementary School: Learning TogetherAlbertville Elementary School: Learning Together
Albertville Elementary School: Learning TogetherDarren Kuropatwa
 
Digital Ethics or The End of The Age of Legends v5.2
 Digital Ethics or The End of The Age of Legends v5.2 Digital Ethics or The End of The Age of Legends v5.2
Digital Ethics or The End of The Age of Legends v5.2Darren Kuropatwa
 

Mehr von Darren Kuropatwa (20)

Digital Storytelling for Deeper Learning v1
Digital Storytelling for Deeper Learning v1Digital Storytelling for Deeper Learning v1
Digital Storytelling for Deeper Learning v1
 
Tales of Learning and the Gifts of Footprints v4.2
Tales of Learning and the Gifts of Footprints v4.2Tales of Learning and the Gifts of Footprints v4.2
Tales of Learning and the Gifts of Footprints v4.2
 
The Fourth Screen v4.2
The Fourth Screen v4.2The Fourth Screen v4.2
The Fourth Screen v4.2
 
Making Student Thinking Visible v4
 Making Student Thinking Visible v4 Making Student Thinking Visible v4
Making Student Thinking Visible v4
 
Learning is at BYTE 2017
Learning is at BYTE 2017Learning is at BYTE 2017
Learning is at BYTE 2017
 
Leveraging Digital for Deeper Learning
Leveraging Digital for Deeper LearningLeveraging Digital for Deeper Learning
Leveraging Digital for Deeper Learning
 
We Learn Through Stories at PRIZMAH17
We Learn Through Stories at PRIZMAH17We Learn Through Stories at PRIZMAH17
We Learn Through Stories at PRIZMAH17
 
Providing Permission to Wonder v3
Providing Permission to Wonder v3Providing Permission to Wonder v3
Providing Permission to Wonder v3
 
The Fourth Screen v4.1
The Fourth Screen v4.1The Fourth Screen v4.1
The Fourth Screen v4.1
 
Making Student Thinking Visible v3.7
 Making Student Thinking Visible v3.7 Making Student Thinking Visible v3.7
Making Student Thinking Visible v3.7
 
Learning is at AUHSD
Learning is at AUHSDLearning is at AUHSD
Learning is at AUHSD
 
Providing Permission to Wonder v2
Providing Permission to Wonder v2Providing Permission to Wonder v2
Providing Permission to Wonder v2
 
The Fourth Screen v4
The Fourth Screen v4The Fourth Screen v4
The Fourth Screen v4
 
Learning is at BLC16
Learning is at BLC16Learning is at BLC16
Learning is at BLC16
 
We Learn Through Stories v4 (master class)
We Learn Through Stories v4 (master class)We Learn Through Stories v4 (master class)
We Learn Through Stories v4 (master class)
 
Deep Learning Design: the middle ring
Deep Learning Design: the middle ringDeep Learning Design: the middle ring
Deep Learning Design: the middle ring
 
Exploring Inquiry
Exploring InquiryExploring Inquiry
Exploring Inquiry
 
HSD Digital Citizenship Framework
HSD Digital Citizenship FrameworkHSD Digital Citizenship Framework
HSD Digital Citizenship Framework
 
Albertville Elementary School: Learning Together
Albertville Elementary School: Learning TogetherAlbertville Elementary School: Learning Together
Albertville Elementary School: Learning Together
 
Digital Ethics or The End of The Age of Legends v5.2
 Digital Ethics or The End of The Age of Legends v5.2 Digital Ethics or The End of The Age of Legends v5.2
Digital Ethics or The End of The Age of Legends v5.2
 

Kürzlich hochgeladen

Man or Manufactured_ Redefining Humanity Through Biopunk Narratives.pptx
Man or Manufactured_ Redefining Humanity Through Biopunk Narratives.pptxMan or Manufactured_ Redefining Humanity Through Biopunk Narratives.pptx
Man or Manufactured_ Redefining Humanity Through Biopunk Narratives.pptxDhatriParmar
 
Student Profile Sample - We help schools to connect the data they have, with ...
Student Profile Sample - We help schools to connect the data they have, with ...Student Profile Sample - We help schools to connect the data they have, with ...
Student Profile Sample - We help schools to connect the data they have, with ...Seán Kennedy
 
Decoding the Tweet _ Practical Criticism in the Age of Hashtag.pptx
Decoding the Tweet _ Practical Criticism in the Age of Hashtag.pptxDecoding the Tweet _ Practical Criticism in the Age of Hashtag.pptx
Decoding the Tweet _ Practical Criticism in the Age of Hashtag.pptxDhatriParmar
 
Multi Domain Alias In the Odoo 17 ERP Module
Multi Domain Alias In the Odoo 17 ERP ModuleMulti Domain Alias In the Odoo 17 ERP Module
Multi Domain Alias In the Odoo 17 ERP ModuleCeline George
 
4.16.24 Poverty and Precarity--Desmond.pptx
4.16.24 Poverty and Precarity--Desmond.pptx4.16.24 Poverty and Precarity--Desmond.pptx
4.16.24 Poverty and Precarity--Desmond.pptxmary850239
 
Concurrency Control in Database Management system
Concurrency Control in Database Management systemConcurrency Control in Database Management system
Concurrency Control in Database Management systemChristalin Nelson
 
How to Fix XML SyntaxError in Odoo the 17
How to Fix XML SyntaxError in Odoo the 17How to Fix XML SyntaxError in Odoo the 17
How to Fix XML SyntaxError in Odoo the 17Celine George
 
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...DhatriParmar
 
week 1 cookery 8 fourth - quarter .pptx
week 1 cookery 8  fourth  -  quarter .pptxweek 1 cookery 8  fourth  -  quarter .pptx
week 1 cookery 8 fourth - quarter .pptxJonalynLegaspi2
 
Mental Health Awareness - a toolkit for supporting young minds
Mental Health Awareness - a toolkit for supporting young mindsMental Health Awareness - a toolkit for supporting young minds
Mental Health Awareness - a toolkit for supporting young mindsPooky Knightsmith
 
Mythology Quiz-4th April 2024, Quiz Club NITW
Mythology Quiz-4th April 2024, Quiz Club NITWMythology Quiz-4th April 2024, Quiz Club NITW
Mythology Quiz-4th April 2024, Quiz Club NITWQuiz Club NITW
 
Narcotic and Non Narcotic Analgesic..pdf
Narcotic and Non Narcotic Analgesic..pdfNarcotic and Non Narcotic Analgesic..pdf
Narcotic and Non Narcotic Analgesic..pdfPrerana Jadhav
 
Congestive Cardiac Failure..presentation
Congestive Cardiac Failure..presentationCongestive Cardiac Failure..presentation
Congestive Cardiac Failure..presentationdeepaannamalai16
 
Unraveling Hypertext_ Analyzing Postmodern Elements in Literature.pptx
Unraveling Hypertext_ Analyzing  Postmodern Elements in  Literature.pptxUnraveling Hypertext_ Analyzing  Postmodern Elements in  Literature.pptx
Unraveling Hypertext_ Analyzing Postmodern Elements in Literature.pptxDhatriParmar
 
Grade Three -ELLNA-REVIEWER-ENGLISH.pptx
Grade Three -ELLNA-REVIEWER-ENGLISH.pptxGrade Three -ELLNA-REVIEWER-ENGLISH.pptx
Grade Three -ELLNA-REVIEWER-ENGLISH.pptxkarenfajardo43
 
Transaction Management in Database Management System
Transaction Management in Database Management SystemTransaction Management in Database Management System
Transaction Management in Database Management SystemChristalin Nelson
 
Oppenheimer Film Discussion for Philosophy and Film
Oppenheimer Film Discussion for Philosophy and FilmOppenheimer Film Discussion for Philosophy and Film
Oppenheimer Film Discussion for Philosophy and FilmStan Meyer
 
Scientific Writing :Research Discourse
Scientific  Writing :Research  DiscourseScientific  Writing :Research  Discourse
Scientific Writing :Research DiscourseAnita GoswamiGiri
 

Kürzlich hochgeladen (20)

Man or Manufactured_ Redefining Humanity Through Biopunk Narratives.pptx
Man or Manufactured_ Redefining Humanity Through Biopunk Narratives.pptxMan or Manufactured_ Redefining Humanity Through Biopunk Narratives.pptx
Man or Manufactured_ Redefining Humanity Through Biopunk Narratives.pptx
 
Student Profile Sample - We help schools to connect the data they have, with ...
Student Profile Sample - We help schools to connect the data they have, with ...Student Profile Sample - We help schools to connect the data they have, with ...
Student Profile Sample - We help schools to connect the data they have, with ...
 
Decoding the Tweet _ Practical Criticism in the Age of Hashtag.pptx
Decoding the Tweet _ Practical Criticism in the Age of Hashtag.pptxDecoding the Tweet _ Practical Criticism in the Age of Hashtag.pptx
Decoding the Tweet _ Practical Criticism in the Age of Hashtag.pptx
 
Multi Domain Alias In the Odoo 17 ERP Module
Multi Domain Alias In the Odoo 17 ERP ModuleMulti Domain Alias In the Odoo 17 ERP Module
Multi Domain Alias In the Odoo 17 ERP Module
 
4.16.24 Poverty and Precarity--Desmond.pptx
4.16.24 Poverty and Precarity--Desmond.pptx4.16.24 Poverty and Precarity--Desmond.pptx
4.16.24 Poverty and Precarity--Desmond.pptx
 
Concurrency Control in Database Management system
Concurrency Control in Database Management systemConcurrency Control in Database Management system
Concurrency Control in Database Management system
 
Paradigm shift in nursing research by RS MEHTA
Paradigm shift in nursing research by RS MEHTAParadigm shift in nursing research by RS MEHTA
Paradigm shift in nursing research by RS MEHTA
 
How to Fix XML SyntaxError in Odoo the 17
How to Fix XML SyntaxError in Odoo the 17How to Fix XML SyntaxError in Odoo the 17
How to Fix XML SyntaxError in Odoo the 17
 
Mattingly "AI & Prompt Design: Large Language Models"
Mattingly "AI & Prompt Design: Large Language Models"Mattingly "AI & Prompt Design: Large Language Models"
Mattingly "AI & Prompt Design: Large Language Models"
 
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...
 
week 1 cookery 8 fourth - quarter .pptx
week 1 cookery 8  fourth  -  quarter .pptxweek 1 cookery 8  fourth  -  quarter .pptx
week 1 cookery 8 fourth - quarter .pptx
 
Mental Health Awareness - a toolkit for supporting young minds
Mental Health Awareness - a toolkit for supporting young mindsMental Health Awareness - a toolkit for supporting young minds
Mental Health Awareness - a toolkit for supporting young minds
 
Mythology Quiz-4th April 2024, Quiz Club NITW
Mythology Quiz-4th April 2024, Quiz Club NITWMythology Quiz-4th April 2024, Quiz Club NITW
Mythology Quiz-4th April 2024, Quiz Club NITW
 
Narcotic and Non Narcotic Analgesic..pdf
Narcotic and Non Narcotic Analgesic..pdfNarcotic and Non Narcotic Analgesic..pdf
Narcotic and Non Narcotic Analgesic..pdf
 
Congestive Cardiac Failure..presentation
Congestive Cardiac Failure..presentationCongestive Cardiac Failure..presentation
Congestive Cardiac Failure..presentation
 
Unraveling Hypertext_ Analyzing Postmodern Elements in Literature.pptx
Unraveling Hypertext_ Analyzing  Postmodern Elements in  Literature.pptxUnraveling Hypertext_ Analyzing  Postmodern Elements in  Literature.pptx
Unraveling Hypertext_ Analyzing Postmodern Elements in Literature.pptx
 
Grade Three -ELLNA-REVIEWER-ENGLISH.pptx
Grade Three -ELLNA-REVIEWER-ENGLISH.pptxGrade Three -ELLNA-REVIEWER-ENGLISH.pptx
Grade Three -ELLNA-REVIEWER-ENGLISH.pptx
 
Transaction Management in Database Management System
Transaction Management in Database Management SystemTransaction Management in Database Management System
Transaction Management in Database Management System
 
Oppenheimer Film Discussion for Philosophy and Film
Oppenheimer Film Discussion for Philosophy and FilmOppenheimer Film Discussion for Philosophy and Film
Oppenheimer Film Discussion for Philosophy and Film
 
Scientific Writing :Research Discourse
Scientific  Writing :Research  DiscourseScientific  Writing :Research  Discourse
Scientific Writing :Research Discourse
 

AP Calculus February 4, 2009