SlideShare a Scribd company logo
Summary of Integration Techniques
                          b
      FTC part II:            F (x) dx = F (b) − F (a)
                      a
      Antiderivatives Table
      Substitution:           f (u(x)) · u (x) dx =    f (u) du

      Integration by Parts:           u dv = u · v −     v du, or

              f (x) · g (x) dx = f (x) · g (x) −         f (x) · g (x) dx

      Trigonometric Integrals: use a trigonometric substitution, a
      trigonometric identity or both.
                               polynomial
      Partial Fractions for                dx ; factor denominator,
                               polynomial
      decompose into partial fractions, integrate
      Approximate Integration
      + any combination thereof.

More Related Content

What's hot

Area between curves
Area between curvesArea between curves
Area between curves
jnaveena j
 
32 stoke's theorem
32 stoke's theorem32 stoke's theorem
32 stoke's theoremmath267
 
Calculus cheat sheet_integrals
Calculus cheat sheet_integralsCalculus cheat sheet_integrals
Calculus cheat sheet_integralsUrbanX4
 
25 the ratio, root, and ratio comparison test x
25 the ratio, root, and ratio  comparison test x25 the ratio, root, and ratio  comparison test x
25 the ratio, root, and ratio comparison test x
math266
 
Lesson 10: the Product and Quotient Rules
Lesson 10: the Product and Quotient RulesLesson 10: the Product and Quotient Rules
Lesson 10: the Product and Quotient Rules
Matthew Leingang
 
Lesson 13: Related Rates Problems
Lesson 13: Related Rates ProblemsLesson 13: Related Rates Problems
Lesson 13: Related Rates ProblemsMatthew Leingang
 
Integration by Parts & by Partial Fractions
Integration by Parts & by Partial FractionsIntegration by Parts & by Partial Fractions
Integration by Parts & by Partial Fractions
MuhammadAliSiddique1
 
Application Of Derivative In Real Life.
Application Of Derivative In Real Life.Application Of Derivative In Real Life.
Application Of Derivative In Real Life.
Afnanul Hassan
 
Common derivatives integrals_reduced
Common derivatives integrals_reducedCommon derivatives integrals_reduced
Common derivatives integrals_reduced
Kyro Fitkry
 
6161103 7.2 shear and moment equations and diagrams
6161103 7.2 shear and moment equations and diagrams6161103 7.2 shear and moment equations and diagrams
6161103 7.2 shear and moment equations and diagramsetcenterrbru
 
Galerkin method
Galerkin methodGalerkin method
Galerkin method
mullerasmare
 
Deriving the composition of functions
Deriving the composition of functionsDeriving the composition of functions
Deriving the composition of functions
Alona Hall
 
27 power series x
27 power series x27 power series x
27 power series x
math266
 
Calculus ppt on "Partial Differentiation"#2
Calculus ppt on "Partial Differentiation"#2Calculus ppt on "Partial Differentiation"#2
Calculus ppt on "Partial Differentiation"#2
L.D College of Engineering
 
Mid term paper of Maths class VI 2011 Fazaia Inter college
Mid term  paper of Maths class  VI 2011 Fazaia Inter collegeMid term  paper of Maths class  VI 2011 Fazaia Inter college
Mid term paper of Maths class VI 2011 Fazaia Inter college
Asad Shafat
 
Lesson 2: Limits and Limit Laws
Lesson 2: Limits and Limit LawsLesson 2: Limits and Limit Laws
Lesson 2: Limits and Limit Laws
Matthew Leingang
 
Indefinite Integral
Indefinite IntegralIndefinite Integral
Indefinite IntegralJelaiAujero
 
Lesson 8 the definite integrals
Lesson 8 the definite integralsLesson 8 the definite integrals
Lesson 8 the definite integrals
Lawrence De Vera
 

What's hot (20)

Area between curves
Area between curvesArea between curves
Area between curves
 
32 stoke's theorem
32 stoke's theorem32 stoke's theorem
32 stoke's theorem
 
Calculus cheat sheet_integrals
Calculus cheat sheet_integralsCalculus cheat sheet_integrals
Calculus cheat sheet_integrals
 
25 the ratio, root, and ratio comparison test x
25 the ratio, root, and ratio  comparison test x25 the ratio, root, and ratio  comparison test x
25 the ratio, root, and ratio comparison test x
 
Lesson 10: the Product and Quotient Rules
Lesson 10: the Product and Quotient RulesLesson 10: the Product and Quotient Rules
Lesson 10: the Product and Quotient Rules
 
Lesson 13: Related Rates Problems
Lesson 13: Related Rates ProblemsLesson 13: Related Rates Problems
Lesson 13: Related Rates Problems
 
Integration by Parts & by Partial Fractions
Integration by Parts & by Partial FractionsIntegration by Parts & by Partial Fractions
Integration by Parts & by Partial Fractions
 
Application Of Derivative In Real Life.
Application Of Derivative In Real Life.Application Of Derivative In Real Life.
Application Of Derivative In Real Life.
 
Common derivatives integrals_reduced
Common derivatives integrals_reducedCommon derivatives integrals_reduced
Common derivatives integrals_reduced
 
6161103 7.2 shear and moment equations and diagrams
6161103 7.2 shear and moment equations and diagrams6161103 7.2 shear and moment equations and diagrams
6161103 7.2 shear and moment equations and diagrams
 
Galerkin method
Galerkin methodGalerkin method
Galerkin method
 
Deriving the composition of functions
Deriving the composition of functionsDeriving the composition of functions
Deriving the composition of functions
 
27 power series x
27 power series x27 power series x
27 power series x
 
Calculus ppt on "Partial Differentiation"#2
Calculus ppt on "Partial Differentiation"#2Calculus ppt on "Partial Differentiation"#2
Calculus ppt on "Partial Differentiation"#2
 
Truss examples
Truss examplesTruss examples
Truss examples
 
11365.integral 2
11365.integral 211365.integral 2
11365.integral 2
 
Mid term paper of Maths class VI 2011 Fazaia Inter college
Mid term  paper of Maths class  VI 2011 Fazaia Inter collegeMid term  paper of Maths class  VI 2011 Fazaia Inter college
Mid term paper of Maths class VI 2011 Fazaia Inter college
 
Lesson 2: Limits and Limit Laws
Lesson 2: Limits and Limit LawsLesson 2: Limits and Limit Laws
Lesson 2: Limits and Limit Laws
 
Indefinite Integral
Indefinite IntegralIndefinite Integral
Indefinite Integral
 
Lesson 8 the definite integrals
Lesson 8 the definite integralsLesson 8 the definite integrals
Lesson 8 the definite integrals
 

Recently uploaded

Overview on Edible Vaccine: Pros & Cons with Mechanism
Overview on Edible Vaccine: Pros & Cons with MechanismOverview on Edible Vaccine: Pros & Cons with Mechanism
Overview on Edible Vaccine: Pros & Cons with Mechanism
DeeptiGupta154
 
How to Split Bills in the Odoo 17 POS Module
How to Split Bills in the Odoo 17 POS ModuleHow to Split Bills in the Odoo 17 POS Module
How to Split Bills in the Odoo 17 POS Module
Celine George
 
Digital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and ResearchDigital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and Research
Vikramjit Singh
 
Synthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptxSynthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptx
Pavel ( NSTU)
 
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
siemaillard
 
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
MysoreMuleSoftMeetup
 
Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345
beazzy04
 
The geography of Taylor Swift - some ideas
The geography of Taylor Swift - some ideasThe geography of Taylor Swift - some ideas
The geography of Taylor Swift - some ideas
GeoBlogs
 
1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx
JosvitaDsouza2
 
Palestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptxPalestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptx
RaedMohamed3
 
How to Break the cycle of negative Thoughts
How to Break the cycle of negative ThoughtsHow to Break the cycle of negative Thoughts
How to Break the cycle of negative Thoughts
Col Mukteshwar Prasad
 
MARUTI SUZUKI- A Successful Joint Venture in India.pptx
MARUTI SUZUKI- A Successful Joint Venture in India.pptxMARUTI SUZUKI- A Successful Joint Venture in India.pptx
MARUTI SUZUKI- A Successful Joint Venture in India.pptx
bennyroshan06
 
The French Revolution Class 9 Study Material pdf free download
The French Revolution Class 9 Study Material pdf free downloadThe French Revolution Class 9 Study Material pdf free download
The French Revolution Class 9 Study Material pdf free download
Vivekanand Anglo Vedic Academy
 
Supporting (UKRI) OA monographs at Salford.pptx
Supporting (UKRI) OA monographs at Salford.pptxSupporting (UKRI) OA monographs at Salford.pptx
Supporting (UKRI) OA monographs at Salford.pptx
Jisc
 
Sectors of the Indian Economy - Class 10 Study Notes pdf
Sectors of the Indian Economy - Class 10 Study Notes pdfSectors of the Indian Economy - Class 10 Study Notes pdf
Sectors of the Indian Economy - Class 10 Study Notes pdf
Vivekanand Anglo Vedic Academy
 
CLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCE
CLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCECLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCE
CLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCE
BhavyaRajput3
 
Additional Benefits for Employee Website.pdf
Additional Benefits for Employee Website.pdfAdditional Benefits for Employee Website.pdf
Additional Benefits for Employee Website.pdf
joachimlavalley1
 
Thesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.pptThesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.ppt
EverAndrsGuerraGuerr
 
Fish and Chips - have they had their chips
Fish and Chips - have they had their chipsFish and Chips - have they had their chips
Fish and Chips - have they had their chips
GeoBlogs
 
PART A. Introduction to Costumer Service
PART A. Introduction to Costumer ServicePART A. Introduction to Costumer Service
PART A. Introduction to Costumer Service
PedroFerreira53928
 

Recently uploaded (20)

Overview on Edible Vaccine: Pros & Cons with Mechanism
Overview on Edible Vaccine: Pros & Cons with MechanismOverview on Edible Vaccine: Pros & Cons with Mechanism
Overview on Edible Vaccine: Pros & Cons with Mechanism
 
How to Split Bills in the Odoo 17 POS Module
How to Split Bills in the Odoo 17 POS ModuleHow to Split Bills in the Odoo 17 POS Module
How to Split Bills in the Odoo 17 POS Module
 
Digital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and ResearchDigital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and Research
 
Synthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptxSynthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptx
 
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
 
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
 
Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345
 
The geography of Taylor Swift - some ideas
The geography of Taylor Swift - some ideasThe geography of Taylor Swift - some ideas
The geography of Taylor Swift - some ideas
 
1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx
 
Palestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptxPalestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptx
 
How to Break the cycle of negative Thoughts
How to Break the cycle of negative ThoughtsHow to Break the cycle of negative Thoughts
How to Break the cycle of negative Thoughts
 
MARUTI SUZUKI- A Successful Joint Venture in India.pptx
MARUTI SUZUKI- A Successful Joint Venture in India.pptxMARUTI SUZUKI- A Successful Joint Venture in India.pptx
MARUTI SUZUKI- A Successful Joint Venture in India.pptx
 
The French Revolution Class 9 Study Material pdf free download
The French Revolution Class 9 Study Material pdf free downloadThe French Revolution Class 9 Study Material pdf free download
The French Revolution Class 9 Study Material pdf free download
 
Supporting (UKRI) OA monographs at Salford.pptx
Supporting (UKRI) OA monographs at Salford.pptxSupporting (UKRI) OA monographs at Salford.pptx
Supporting (UKRI) OA monographs at Salford.pptx
 
Sectors of the Indian Economy - Class 10 Study Notes pdf
Sectors of the Indian Economy - Class 10 Study Notes pdfSectors of the Indian Economy - Class 10 Study Notes pdf
Sectors of the Indian Economy - Class 10 Study Notes pdf
 
CLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCE
CLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCECLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCE
CLASS 11 CBSE B.St Project AIDS TO TRADE - INSURANCE
 
Additional Benefits for Employee Website.pdf
Additional Benefits for Employee Website.pdfAdditional Benefits for Employee Website.pdf
Additional Benefits for Employee Website.pdf
 
Thesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.pptThesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.ppt
 
Fish and Chips - have they had their chips
Fish and Chips - have they had their chipsFish and Chips - have they had their chips
Fish and Chips - have they had their chips
 
PART A. Introduction to Costumer Service
PART A. Introduction to Costumer ServicePART A. Introduction to Costumer Service
PART A. Introduction to Costumer Service
 

Summary of Integration Methods

  • 1. Summary of Integration Techniques b FTC part II: F (x) dx = F (b) − F (a) a Antiderivatives Table Substitution: f (u(x)) · u (x) dx = f (u) du Integration by Parts: u dv = u · v − v du, or f (x) · g (x) dx = f (x) · g (x) − f (x) · g (x) dx Trigonometric Integrals: use a trigonometric substitution, a trigonometric identity or both. polynomial Partial Fractions for dx ; factor denominator, polynomial decompose into partial fractions, integrate Approximate Integration + any combination thereof.