SlideShare a Scribd company logo

Lesson 28: The Fundamental Theorem of Calculus

•
•
Matthew Leingang
Matthew Leingang

The Fundamental Theorem of Calculus relates the two essential concepts in calculus.

TechnologyEducation
1 of 67
Download to read offline
Section 5.4 The Fundamental Theorem of Calculus Math 1a Introduction to Calculus April 16, 2008 Announcements Midterm is finished: ¯ ≈ 43, σ ≈ 6. x ◮ Midterm III is Wednesday 4/30 in class ◮ Friday 5/2 is Movie Day! ◮ Problem Sessions Sunday, Thursday, 7pm, SC 310 ◮ Office hours Tues, Weds, 2–4pm SC 323 ◮ . . . . . .
Announcements Midterm is finished: ¯ ≈ 43, σ ≈ 6. x ◮ Midterm III is Wednesday 4/30 in class ◮ Friday 5/2 is Movie Day! ◮ Problem Sessions Sunday, Thursday, 7pm, SC 310 ◮ Office hours Tues, Weds, 2–4pm SC 323 ◮ . . . . . .
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus
Lesson 28: The Fundamental Theorem of Calculus

Recommended

Lesson 27: Evaluating Definite Integrals
Lesson 27: Evaluating Definite IntegralsLesson 27: Evaluating Definite Integrals
Lesson 27: Evaluating Definite IntegralsMatthew Leingang
 
Lesson 31: Numerical Integration
Lesson 31: Numerical IntegrationLesson 31: Numerical Integration
Lesson 31: Numerical IntegrationMatthew Leingang
 
THE NITROGEN CYCLE BY AALOK KUMAR DESHMUKH
THE NITROGEN CYCLE BY AALOK KUMAR DESHMUKHTHE NITROGEN CYCLE BY AALOK KUMAR DESHMUKH
THE NITROGEN CYCLE BY AALOK KUMAR DESHMUKHYaalok
 
Lesson 29: Integration by Substitution
Lesson 29: Integration by SubstitutionLesson 29: Integration by Substitution
Lesson 29: Integration by SubstitutionMatthew Leingang
 
Lesson 25: Areas
Lesson 25: AreasLesson 25: Areas
Lesson 25: AreasMatthew Leingang
 
Lesson 24: Antiderivatives
Lesson 24: AntiderivativesLesson 24: Antiderivatives
Lesson 24: AntiderivativesMatthew Leingang
 
Introduction
IntroductionIntroduction
IntroductionMatthew Leingang
 
Lesson 21: Surface Area
Lesson 21: Surface AreaLesson 21: Surface Area
Lesson 21: Surface AreaMatthew Leingang
 

Recommended

Lesson 27: Evaluating Definite Integrals
Lesson 27: Evaluating Definite IntegralsLesson 27: Evaluating Definite Integrals
Lesson 27: Evaluating Definite IntegralsMatthew Leingang
 
Lesson 31: Numerical Integration
Lesson 31: Numerical IntegrationLesson 31: Numerical Integration
Lesson 31: Numerical IntegrationMatthew Leingang
 
THE NITROGEN CYCLE BY AALOK KUMAR DESHMUKH
THE NITROGEN CYCLE BY AALOK KUMAR DESHMUKHTHE NITROGEN CYCLE BY AALOK KUMAR DESHMUKH
THE NITROGEN CYCLE BY AALOK KUMAR DESHMUKHYaalok
 
Lesson 29: Integration by Substitution
Lesson 29: Integration by SubstitutionLesson 29: Integration by Substitution
Lesson 29: Integration by SubstitutionMatthew Leingang
 
Lesson 25: Areas
Lesson 25: AreasLesson 25: Areas
Lesson 25: AreasMatthew Leingang
 
Lesson 24: Antiderivatives
Lesson 24: AntiderivativesLesson 24: Antiderivatives
Lesson 24: AntiderivativesMatthew Leingang
 
Introduction
IntroductionIntroduction
IntroductionMatthew Leingang
 
Lesson 21: Surface Area
Lesson 21: Surface AreaLesson 21: Surface Area
Lesson 21: Surface AreaMatthew Leingang
 
Lesson 23: Newton's Method
Lesson 23: Newton's MethodLesson 23: Newton's Method
Lesson 23: Newton's MethodMatthew Leingang
 
Lesson 22: Triple Integrals
Lesson 22: Triple IntegralsLesson 22: Triple Integrals
Lesson 22: Triple IntegralsMatthew Leingang
 
Lesson 15: Linear Approximation and Differentials
Lesson 15: Linear Approximation and DifferentialsLesson 15: Linear Approximation and Differentials
Lesson 15: Linear Approximation and DifferentialsMatthew Leingang
 
Inquiry-Based Learning Opportunities for Secondary Teachers and Students
Inquiry-Based Learning Opportunities for Secondary Teachers and StudentsInquiry-Based Learning Opportunities for Secondary Teachers and Students
Inquiry-Based Learning Opportunities for Secondary Teachers and StudentsMatthew Leingang
 
Lesson 15: Gradients and level curves
Lesson 15: Gradients and level curvesLesson 15: Gradients and level curves
Lesson 15: Gradients and level curvesMatthew Leingang
 
Lesson 22: Applications to Business and Economics
Lesson 22: Applications to Business and EconomicsLesson 22: Applications to Business and Economics
Lesson 22: Applications to Business and EconomicsMatthew Leingang
 
Lesson 27: The Fundamental Theorem of Calculus
Lesson 27: The Fundamental Theorem of CalculusLesson 27: The Fundamental Theorem of Calculus
Lesson 27: The Fundamental Theorem of CalculusMatthew Leingang
 
Math major 14 differential calculus pw
Math major 14 differential calculus pwMath major 14 differential calculus pw
Math major 14 differential calculus pwReymart Bargamento
 
Final Review II
Final Review IIFinal Review II
Final Review IIMatthew Leingang
 
Lesson 30: Stokes's Theorem
Lesson 30: Stokes's TheoremLesson 30: Stokes's Theorem
Lesson 30: Stokes's TheoremMatthew Leingang
 
Lesson 30: Integration by Parts
Lesson 30: Integration by PartsLesson 30: Integration by Parts
Lesson 30: Integration by PartsMatthew Leingang
 
Microbe presentation
Microbe presentationMicrobe presentation
Microbe presentationLiana Harotian
 
Lesson 1: Functions
Lesson 1: FunctionsLesson 1: Functions
Lesson 1: FunctionsMatthew Leingang
 
Lesson 20: Integration in Polar Coordinates
Lesson 20: Integration in Polar CoordinatesLesson 20: Integration in Polar Coordinates
Lesson 20: Integration in Polar CoordinatesMatthew Leingang
 
Lesson 21: Indeterminate forms and L'Hôpital's Rule
Lesson 21: Indeterminate forms and L'Hôpital's RuleLesson 21: Indeterminate forms and L'Hôpital's Rule
Lesson 21: Indeterminate forms and L'Hôpital's RuleMatthew Leingang
 
Lesson 26: The Definite Integral
Lesson 26: The Definite IntegralLesson 26: The Definite Integral
Lesson 26: The Definite IntegralMatthew Leingang
 
Lesson 31: The Divergence Theorem
Lesson 31: The Divergence TheoremLesson 31: The Divergence Theorem
Lesson 31: The Divergence TheoremMatthew Leingang
 
Build Features, Not Apps
Build Features, Not AppsBuild Features, Not Apps
Build Features, Not AppsNatasha Murashev
 
Making Lesson Plans
Making Lesson PlansMaking Lesson Plans
Making Lesson PlansMatthew Leingang
 
Streamlining assessment, feedback, and archival with auto-multiple-choice
Streamlining assessment, feedback, and archival with auto-multiple-choiceStreamlining assessment, feedback, and archival with auto-multiple-choice
Streamlining assessment, feedback, and archival with auto-multiple-choiceMatthew Leingang
 
Electronic Grading of Paper Assessments
Electronic Grading of Paper AssessmentsElectronic Grading of Paper Assessments
Electronic Grading of Paper AssessmentsMatthew Leingang
 
Lesson 27: Integration by Substitution (slides)
Lesson 27: Integration by Substitution (slides)Lesson 27: Integration by Substitution (slides)
Lesson 27: Integration by Substitution (slides)Matthew Leingang
 

More Related Content

Viewers also liked

Lesson 23: Newton's Method
Lesson 23: Newton's MethodLesson 23: Newton's Method
Lesson 23: Newton's MethodMatthew Leingang
 
Lesson 22: Triple Integrals
Lesson 22: Triple IntegralsLesson 22: Triple Integrals
Lesson 22: Triple IntegralsMatthew Leingang
 
Lesson 15: Linear Approximation and Differentials
Lesson 15: Linear Approximation and DifferentialsLesson 15: Linear Approximation and Differentials
Lesson 15: Linear Approximation and DifferentialsMatthew Leingang
 
Inquiry-Based Learning Opportunities for Secondary Teachers and Students
Inquiry-Based Learning Opportunities for Secondary Teachers and StudentsInquiry-Based Learning Opportunities for Secondary Teachers and Students
Inquiry-Based Learning Opportunities for Secondary Teachers and StudentsMatthew Leingang
 
Lesson 15: Gradients and level curves
Lesson 15: Gradients and level curvesLesson 15: Gradients and level curves
Lesson 15: Gradients and level curvesMatthew Leingang
 
Lesson 22: Applications to Business and Economics
Lesson 22: Applications to Business and EconomicsLesson 22: Applications to Business and Economics
Lesson 22: Applications to Business and EconomicsMatthew Leingang
 
Lesson 27: The Fundamental Theorem of Calculus
Lesson 27: The Fundamental Theorem of CalculusLesson 27: The Fundamental Theorem of Calculus
Lesson 27: The Fundamental Theorem of CalculusMatthew Leingang
 
Math major 14 differential calculus pw
Math major 14 differential calculus pwMath major 14 differential calculus pw
Math major 14 differential calculus pwReymart Bargamento
 
Lesson 30: Stokes's Theorem
Lesson 30: Stokes's TheoremLesson 30: Stokes's Theorem
Lesson 30: Stokes's TheoremMatthew Leingang
 
Lesson 30: Integration by Parts
Lesson 30: Integration by PartsLesson 30: Integration by Parts
Lesson 30: Integration by PartsMatthew Leingang
 
Lesson 20: Integration in Polar Coordinates
Lesson 20: Integration in Polar CoordinatesLesson 20: Integration in Polar Coordinates
Lesson 20: Integration in Polar CoordinatesMatthew Leingang
 
Lesson 21: Indeterminate forms and L'Hôpital's Rule
Lesson 21: Indeterminate forms and L'Hôpital's RuleLesson 21: Indeterminate forms and L'Hôpital's Rule
Lesson 21: Indeterminate forms and L'Hôpital's RuleMatthew Leingang
 
Lesson 26: The Definite Integral
Lesson 26: The Definite IntegralLesson 26: The Definite Integral
Lesson 26: The Definite IntegralMatthew Leingang
 
Lesson 31: The Divergence Theorem
Lesson 31: The Divergence TheoremLesson 31: The Divergence Theorem
Lesson 31: The Divergence TheoremMatthew Leingang
 

Viewers also liked (18)

Lesson 23: Newton's Method
Lesson 23: Newton's MethodLesson 23: Newton's Method
Lesson 23: Newton's Method
 
Lesson 22: Triple Integrals
Lesson 22: Triple IntegralsLesson 22: Triple Integrals
Lesson 22: Triple Integrals
 
Lesson 15: Linear Approximation and Differentials
Lesson 15: Linear Approximation and DifferentialsLesson 15: Linear Approximation and Differentials
Lesson 15: Linear Approximation and Differentials
 
Inquiry-Based Learning Opportunities for Secondary Teachers and Students
Inquiry-Based Learning Opportunities for Secondary Teachers and StudentsInquiry-Based Learning Opportunities for Secondary Teachers and Students
Inquiry-Based Learning Opportunities for Secondary Teachers and Students
 
Lesson 15: Gradients and level curves
Lesson 15: Gradients and level curvesLesson 15: Gradients and level curves
Lesson 15: Gradients and level curves
 
Lesson 22: Applications to Business and Economics
Lesson 22: Applications to Business and EconomicsLesson 22: Applications to Business and Economics
Lesson 22: Applications to Business and Economics
 
Lesson 27: The Fundamental Theorem of Calculus
Lesson 27: The Fundamental Theorem of CalculusLesson 27: The Fundamental Theorem of Calculus
Lesson 27: The Fundamental Theorem of Calculus
 
Math major 14 differential calculus pw
Math major 14 differential calculus pwMath major 14 differential calculus pw
Math major 14 differential calculus pw
 
Final Review II
Final Review IIFinal Review II
Final Review II
 
Lesson 30: Stokes's Theorem
Lesson 30: Stokes's TheoremLesson 30: Stokes's Theorem
Lesson 30: Stokes's Theorem
 
Lesson 30: Integration by Parts
Lesson 30: Integration by PartsLesson 30: Integration by Parts
Lesson 30: Integration by Parts
 
Microbe presentation
Microbe presentationMicrobe presentation
Microbe presentation
 
Lesson 1: Functions
Lesson 1: FunctionsLesson 1: Functions
Lesson 1: Functions
 
Lesson 20: Integration in Polar Coordinates
Lesson 20: Integration in Polar CoordinatesLesson 20: Integration in Polar Coordinates
Lesson 20: Integration in Polar Coordinates
 
Lesson 21: Indeterminate forms and L'Hôpital's Rule
Lesson 21: Indeterminate forms and L'Hôpital's RuleLesson 21: Indeterminate forms and L'Hôpital's Rule
Lesson 21: Indeterminate forms and L'Hôpital's Rule
 
Lesson 26: The Definite Integral
Lesson 26: The Definite IntegralLesson 26: The Definite Integral
Lesson 26: The Definite Integral
 
Lesson 31: The Divergence Theorem
Lesson 31: The Divergence TheoremLesson 31: The Divergence Theorem
Lesson 31: The Divergence Theorem
 
Build Features, Not Apps
Build Features, Not AppsBuild Features, Not Apps
Build Features, Not Apps
 

More from Matthew Leingang

Streamlining assessment, feedback, and archival with auto-multiple-choice
Streamlining assessment, feedback, and archival with auto-multiple-choiceStreamlining assessment, feedback, and archival with auto-multiple-choice
Streamlining assessment, feedback, and archival with auto-multiple-choiceMatthew Leingang
 
Electronic Grading of Paper Assessments
Electronic Grading of Paper AssessmentsElectronic Grading of Paper Assessments
Electronic Grading of Paper AssessmentsMatthew Leingang
 
Lesson 27: Integration by Substitution (slides)
Lesson 27: Integration by Substitution (slides)Lesson 27: Integration by Substitution (slides)
Lesson 27: Integration by Substitution (slides)Matthew Leingang
 
Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)Matthew Leingang
 
Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)Matthew Leingang
 
Lesson 27: Integration by Substitution (handout)
Lesson 27: Integration by Substitution (handout)Lesson 27: Integration by Substitution (handout)
Lesson 27: Integration by Substitution (handout)Matthew Leingang
 
Lesson 26: The Fundamental Theorem of Calculus (handout)
Lesson 26: The Fundamental Theorem of Calculus (handout)Lesson 26: The Fundamental Theorem of Calculus (handout)
Lesson 26: The Fundamental Theorem of Calculus (handout)Matthew Leingang
 
Lesson 25: Evaluating Definite Integrals (slides)
Lesson 25: Evaluating Definite Integrals (slides)Lesson 25: Evaluating Definite Integrals (slides)
Lesson 25: Evaluating Definite Integrals (slides)Matthew Leingang
 
Lesson 25: Evaluating Definite Integrals (handout)
Lesson 25: Evaluating Definite Integrals (handout)Lesson 25: Evaluating Definite Integrals (handout)
Lesson 25: Evaluating Definite Integrals (handout)Matthew Leingang
 
Lesson 24: Areas and Distances, The Definite Integral (handout)
Lesson 24: Areas and Distances, The Definite Integral (handout)Lesson 24: Areas and Distances, The Definite Integral (handout)
Lesson 24: Areas and Distances, The Definite Integral (handout)Matthew Leingang
 
Lesson 24: Areas and Distances, The Definite Integral (slides)
Lesson 24: Areas and Distances, The Definite Integral (slides)Lesson 24: Areas and Distances, The Definite Integral (slides)
Lesson 24: Areas and Distances, The Definite Integral (slides)Matthew Leingang
 
Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)Matthew Leingang
 
Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)Matthew Leingang
 
Lesson 22: Optimization Problems (slides)
Lesson 22: Optimization Problems (slides)Lesson 22: Optimization Problems (slides)
Lesson 22: Optimization Problems (slides)Matthew Leingang
 
Lesson 22: Optimization Problems (handout)
Lesson 22: Optimization Problems (handout)Lesson 22: Optimization Problems (handout)
Lesson 22: Optimization Problems (handout)Matthew Leingang
 
Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)Matthew Leingang
 
Lesson 21: Curve Sketching (handout)
Lesson 21: Curve Sketching (handout)Lesson 21: Curve Sketching (handout)
Lesson 21: Curve Sketching (handout)Matthew Leingang
 
Lesson 20: Derivatives and the Shapes of Curves (slides)
Lesson 20: Derivatives and the Shapes of Curves (slides)Lesson 20: Derivatives and the Shapes of Curves (slides)
Lesson 20: Derivatives and the Shapes of Curves (slides)Matthew Leingang
 
Lesson 20: Derivatives and the Shapes of Curves (handout)
Lesson 20: Derivatives and the Shapes of Curves (handout)Lesson 20: Derivatives and the Shapes of Curves (handout)
Lesson 20: Derivatives and the Shapes of Curves (handout)Matthew Leingang
 

More from Matthew Leingang (20)

Making Lesson Plans
Making Lesson PlansMaking Lesson Plans
Making Lesson Plans
 
Streamlining assessment, feedback, and archival with auto-multiple-choice
Streamlining assessment, feedback, and archival with auto-multiple-choiceStreamlining assessment, feedback, and archival with auto-multiple-choice
Streamlining assessment, feedback, and archival with auto-multiple-choice
 
Electronic Grading of Paper Assessments
Electronic Grading of Paper AssessmentsElectronic Grading of Paper Assessments
Electronic Grading of Paper Assessments
 
Lesson 27: Integration by Substitution (slides)
Lesson 27: Integration by Substitution (slides)Lesson 27: Integration by Substitution (slides)
Lesson 27: Integration by Substitution (slides)
 
Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)
 
Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)Lesson 26: The Fundamental Theorem of Calculus (slides)
Lesson 26: The Fundamental Theorem of Calculus (slides)
 
Lesson 27: Integration by Substitution (handout)
Lesson 27: Integration by Substitution (handout)Lesson 27: Integration by Substitution (handout)
Lesson 27: Integration by Substitution (handout)
 
Lesson 26: The Fundamental Theorem of Calculus (handout)
Lesson 26: The Fundamental Theorem of Calculus (handout)Lesson 26: The Fundamental Theorem of Calculus (handout)
Lesson 26: The Fundamental Theorem of Calculus (handout)
 
Lesson 25: Evaluating Definite Integrals (slides)
Lesson 25: Evaluating Definite Integrals (slides)Lesson 25: Evaluating Definite Integrals (slides)
Lesson 25: Evaluating Definite Integrals (slides)
 
Lesson 25: Evaluating Definite Integrals (handout)
Lesson 25: Evaluating Definite Integrals (handout)Lesson 25: Evaluating Definite Integrals (handout)
Lesson 25: Evaluating Definite Integrals (handout)
 
Lesson 24: Areas and Distances, The Definite Integral (handout)
Lesson 24: Areas and Distances, The Definite Integral (handout)Lesson 24: Areas and Distances, The Definite Integral (handout)
Lesson 24: Areas and Distances, The Definite Integral (handout)
 
Lesson 24: Areas and Distances, The Definite Integral (slides)
Lesson 24: Areas and Distances, The Definite Integral (slides)Lesson 24: Areas and Distances, The Definite Integral (slides)
Lesson 24: Areas and Distances, The Definite Integral (slides)
 
Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)
 
Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)Lesson 23: Antiderivatives (slides)
Lesson 23: Antiderivatives (slides)
 
Lesson 22: Optimization Problems (slides)
Lesson 22: Optimization Problems (slides)Lesson 22: Optimization Problems (slides)
Lesson 22: Optimization Problems (slides)
 
Lesson 22: Optimization Problems (handout)
Lesson 22: Optimization Problems (handout)Lesson 22: Optimization Problems (handout)
Lesson 22: Optimization Problems (handout)
 
Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)Lesson 21: Curve Sketching (slides)
Lesson 21: Curve Sketching (slides)
 
Lesson 21: Curve Sketching (handout)
Lesson 21: Curve Sketching (handout)Lesson 21: Curve Sketching (handout)
Lesson 21: Curve Sketching (handout)
 
Lesson 20: Derivatives and the Shapes of Curves (slides)
Lesson 20: Derivatives and the Shapes of Curves (slides)Lesson 20: Derivatives and the Shapes of Curves (slides)
Lesson 20: Derivatives and the Shapes of Curves (slides)
 
Lesson 20: Derivatives and the Shapes of Curves (handout)
Lesson 20: Derivatives and the Shapes of Curves (handout)Lesson 20: Derivatives and the Shapes of Curves (handout)
Lesson 20: Derivatives and the Shapes of Curves (handout)
 

Recently uploaded

Apidays Singapore 2024 - Building Digital Trust in a Digital Economy by Veron...
Apidays Singapore 2024 - Building Digital Trust in a Digital Economy by Veron...Apidays Singapore 2024 - Building Digital Trust in a Digital Economy by Veron...
Apidays Singapore 2024 - Building Digital Trust in a Digital Economy by Veron...apidays
 
Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...
Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...
Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...Neo4j
 
Histor y of HAM Radio presentation slide
Histor y of HAM Radio presentation slideHistor y of HAM Radio presentation slide
Histor y of HAM Radio presentation slidevu2urc
 
Axa Assurance Maroc - Insurer Innovation Award 2024
Axa Assurance Maroc - Insurer Innovation Award 2024Axa Assurance Maroc - Insurer Innovation Award 2024
Axa Assurance Maroc - Insurer Innovation Award 2024The Digital Insurer
 
Scaling API-first – The story of a global engineering organization
Scaling API-first – The story of a global engineering organizationScaling API-first – The story of a global engineering organization
Scaling API-first – The story of a global engineering organizationRadu Cotescu
 
Salesforce Community Group Quito, Salesforce 101
Salesforce Community Group Quito, Salesforce 101Salesforce Community Group Quito, Salesforce 101
Salesforce Community Group Quito, Salesforce 101Paola De la Torre
 
Partners Life - Insurer Innovation Award 2024
Partners Life - Insurer Innovation Award 2024Partners Life - Insurer Innovation Award 2024
Partners Life - Insurer Innovation Award 2024The Digital Insurer
 
Automating Google Workspace (GWS) & more with Apps Script
Automating Google Workspace (GWS) & more with Apps ScriptAutomating Google Workspace (GWS) & more with Apps Script
Automating Google Workspace (GWS) & more with Apps Scriptwesley chun
 
08448380779 Call Girls In Diplomatic Enclave Women Seeking Men
08448380779 Call Girls In Diplomatic Enclave Women Seeking Men08448380779 Call Girls In Diplomatic Enclave Women Seeking Men
08448380779 Call Girls In Diplomatic Enclave Women Seeking MenDelhi Call girls
 
IAC 2024 - IA Fast Track to Search Focused AI Solutions
IAC 2024 - IA Fast Track to Search Focused AI SolutionsIAC 2024 - IA Fast Track to Search Focused AI Solutions
IAC 2024 - IA Fast Track to Search Focused AI SolutionsEnterprise Knowledge
 
Developing An App To Navigate The Roads of Brazil
Developing An App To Navigate The Roads of BrazilDeveloping An App To Navigate The Roads of Brazil
Developing An App To Navigate The Roads of BrazilV3cube
 
Workshop - Best of Both Worlds_ Combine KG and Vector search for enhanced R...
Workshop - Best of Both Worlds_ Combine KG and Vector search for enhanced R...Workshop - Best of Both Worlds_ Combine KG and Vector search for enhanced R...
Workshop - Best of Both Worlds_ Combine KG and Vector search for enhanced R...Neo4j
 
How to convert PDF to text with Nanonets
How to convert PDF to text with NanonetsHow to convert PDF to text with Nanonets
How to convert PDF to text with Nanonetsnaman860154
 
WhatsApp 9892124323 ✓Call Girls In Kalyan ( Mumbai ) secure service
WhatsApp 9892124323 ✓Call Girls In Kalyan ( Mumbai ) secure serviceWhatsApp 9892124323 ✓Call Girls In Kalyan ( Mumbai ) secure service
WhatsApp 9892124323 ✓Call Girls In Kalyan ( Mumbai ) secure servicePooja Nehwal
 
Driving Behavioral Change for Information Management through Data-Driven Gree...
Driving Behavioral Change for Information Management through Data-Driven Gree...Driving Behavioral Change for Information Management through Data-Driven Gree...
Driving Behavioral Change for Information Management through Data-Driven Gree...Enterprise Knowledge
 
TrustArc Webinar - Stay Ahead of US State Data Privacy Law Developments
TrustArc Webinar - Stay Ahead of US State Data Privacy Law DevelopmentsTrustArc Webinar - Stay Ahead of US State Data Privacy Law Developments
TrustArc Webinar - Stay Ahead of US State Data Privacy Law DevelopmentsTrustArc
 
Handwritten Text Recognition for manuscripts and early printed texts
Handwritten Text Recognition for manuscripts and early printed textsHandwritten Text Recognition for manuscripts and early printed texts
Handwritten Text Recognition for manuscripts and early printed textsMaria Levchenko
 
[2024]Digital Global Overview Report 2024 Meltwater.pdf
[2024]Digital Global Overview Report 2024 Meltwater.pdf[2024]Digital Global Overview Report 2024 Meltwater.pdf
[2024]Digital Global Overview Report 2024 Meltwater.pdfhans926745
 
Breaking the Kubernetes Kill Chain: Host Path Mount
Breaking the Kubernetes Kill Chain: Host Path MountBreaking the Kubernetes Kill Chain: Host Path Mount
Breaking the Kubernetes Kill Chain: Host Path MountPuma Security, LLC
 
04-2024-HHUG-Sales-and-Marketing-Alignment.pptx
04-2024-HHUG-Sales-and-Marketing-Alignment.pptx04-2024-HHUG-Sales-and-Marketing-Alignment.pptx
04-2024-HHUG-Sales-and-Marketing-Alignment.pptxHampshireHUG
 

Recently uploaded (20)

Apidays Singapore 2024 - Building Digital Trust in a Digital Economy by Veron...
Apidays Singapore 2024 - Building Digital Trust in a Digital Economy by Veron...Apidays Singapore 2024 - Building Digital Trust in a Digital Economy by Veron...
Apidays Singapore 2024 - Building Digital Trust in a Digital Economy by Veron...
 
Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...
Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...
Neo4j - How KGs are shaping the future of Generative AI at AWS Summit London ...
 
Histor y of HAM Radio presentation slide
Histor y of HAM Radio presentation slideHistor y of HAM Radio presentation slide
Histor y of HAM Radio presentation slide
 
Axa Assurance Maroc - Insurer Innovation Award 2024
Axa Assurance Maroc - Insurer Innovation Award 2024Axa Assurance Maroc - Insurer Innovation Award 2024
Axa Assurance Maroc - Insurer Innovation Award 2024
 
Scaling API-first – The story of a global engineering organization
Scaling API-first – The story of a global engineering organizationScaling API-first – The story of a global engineering organization
Scaling API-first – The story of a global engineering organization
 
Salesforce Community Group Quito, Salesforce 101
Salesforce Community Group Quito, Salesforce 101Salesforce Community Group Quito, Salesforce 101
Salesforce Community Group Quito, Salesforce 101
 
Partners Life - Insurer Innovation Award 2024
Partners Life - Insurer Innovation Award 2024Partners Life - Insurer Innovation Award 2024
Partners Life - Insurer Innovation Award 2024
 
Automating Google Workspace (GWS) & more with Apps Script
Automating Google Workspace (GWS) & more with Apps ScriptAutomating Google Workspace (GWS) & more with Apps Script
Automating Google Workspace (GWS) & more with Apps Script
 
08448380779 Call Girls In Diplomatic Enclave Women Seeking Men
08448380779 Call Girls In Diplomatic Enclave Women Seeking Men08448380779 Call Girls In Diplomatic Enclave Women Seeking Men
08448380779 Call Girls In Diplomatic Enclave Women Seeking Men
 
IAC 2024 - IA Fast Track to Search Focused AI Solutions
IAC 2024 - IA Fast Track to Search Focused AI SolutionsIAC 2024 - IA Fast Track to Search Focused AI Solutions
IAC 2024 - IA Fast Track to Search Focused AI Solutions
 
Developing An App To Navigate The Roads of Brazil
Developing An App To Navigate The Roads of BrazilDeveloping An App To Navigate The Roads of Brazil
Developing An App To Navigate The Roads of Brazil
 
Workshop - Best of Both Worlds_ Combine KG and Vector search for enhanced R...
Workshop - Best of Both Worlds_ Combine KG and Vector search for enhanced R...Workshop - Best of Both Worlds_ Combine KG and Vector search for enhanced R...
Workshop - Best of Both Worlds_ Combine KG and Vector search for enhanced R...
 
How to convert PDF to text with Nanonets
How to convert PDF to text with NanonetsHow to convert PDF to text with Nanonets
How to convert PDF to text with Nanonets
 
WhatsApp 9892124323 ✓Call Girls In Kalyan ( Mumbai ) secure service
WhatsApp 9892124323 ✓Call Girls In Kalyan ( Mumbai ) secure serviceWhatsApp 9892124323 ✓Call Girls In Kalyan ( Mumbai ) secure service
WhatsApp 9892124323 ✓Call Girls In Kalyan ( Mumbai ) secure service
 
Driving Behavioral Change for Information Management through Data-Driven Gree...
Driving Behavioral Change for Information Management through Data-Driven Gree...Driving Behavioral Change for Information Management through Data-Driven Gree...
Driving Behavioral Change for Information Management through Data-Driven Gree...
 
TrustArc Webinar - Stay Ahead of US State Data Privacy Law Developments
TrustArc Webinar - Stay Ahead of US State Data Privacy Law DevelopmentsTrustArc Webinar - Stay Ahead of US State Data Privacy Law Developments
TrustArc Webinar - Stay Ahead of US State Data Privacy Law Developments
 
Handwritten Text Recognition for manuscripts and early printed texts
Handwritten Text Recognition for manuscripts and early printed textsHandwritten Text Recognition for manuscripts and early printed texts
Handwritten Text Recognition for manuscripts and early printed texts
 
[2024]Digital Global Overview Report 2024 Meltwater.pdf
[2024]Digital Global Overview Report 2024 Meltwater.pdf[2024]Digital Global Overview Report 2024 Meltwater.pdf
[2024]Digital Global Overview Report 2024 Meltwater.pdf
 
Breaking the Kubernetes Kill Chain: Host Path Mount
Breaking the Kubernetes Kill Chain: Host Path MountBreaking the Kubernetes Kill Chain: Host Path Mount
Breaking the Kubernetes Kill Chain: Host Path Mount
 
04-2024-HHUG-Sales-and-Marketing-Alignment.pptx
04-2024-HHUG-Sales-and-Marketing-Alignment.pptx04-2024-HHUG-Sales-and-Marketing-Alignment.pptx
04-2024-HHUG-Sales-and-Marketing-Alignment.pptx
 

Lesson 28: The Fundamental Theorem of Calculus

  • 1. Section 5.4 The Fundamental Theorem of Calculus Math 1a Introduction to Calculus April 16, 2008 Announcements Midterm is finished: ¯ ≈ 43, σ ≈ 6. x ◮ Midterm III is Wednesday 4/30 in class ◮ Friday 5/2 is Movie Day! ◮ Problem Sessions Sunday, Thursday, 7pm, SC 310 ◮ Office hours Tues, Weds, 2–4pm SC 323 ◮ . . . . . .
  • 2. Announcements Midterm is finished: ¯ ≈ 43, σ ≈ 6. x ◮ Midterm III is Wednesday 4/30 in class ◮ Friday 5/2 is Movie Day! ◮ Problem Sessions Sunday, Thursday, 7pm, SC 310 ◮ Office hours Tues, Weds, 2–4pm SC 323 ◮ . . . . . .