Definite Integrals and Antiderivatives

Slides:



Advertisements
Similar presentations
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 1.
Advertisements

Section 4.3 Indefinite Integrals and Net Change Theorem Math 1231: Single-Variable Calculus.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 5.4 Fundamental Theorem of Calculus.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 1.
5.4 Fundamental Theorem of Calculus Quick Review.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 5.1 Estimating with Finite Sums.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 6.3 Antidifferentiation by Parts.
Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1 Section 6.4 Fundamental Theorem of Calculus Applications of Derivatives Chapter 6.
5.3 Definite Integrals and Antiderivatives. What you’ll learn about Properties of Definite Integrals Average Value of a Function Mean Value Theorem for.
Fundamental Theorem of Calculus
Section 6.2* The Natural Logarithmic Function. THE NATURAL LOGARITHMIC FUNCTION.
Slide 5- 1 Quick Review. Slide 5- 2 Quick Review Solutions.
MTH 252 Integral Calculus Chapter 6 – Integration Section 6.6 – The Fundamental Theorem of Calculus Copyright © 2005 by Ron Wallace, all rights reserved.
The Fundamental Theorem of Calculus is appropriately named because it establishes connection between the two branches of calculus: differential calculus.
Integrals. The re-construction of a function from its derivative is anti-differentiation integration OR.
Chapter Five Integration.
Rules for Differentiation
Chapter 5 The Definite Integral. Chapter 5 The Definite Integral.
Derivatives of Exponential and Logarithmic Functions
Quick Review.
Definite Integrals and Antiderivatives
MTH1170 The Fundamental Theorem of Calculus
4.4 The Fundamental Theorem of Calculus
Rates of Change and Limits
Estimating with Finite Sums
Chapter 5 Integrals.
Rules for Differentiation
Rules for Differentiation
Unit 6 – Fundamentals of Calculus Section 6
Review  .
Integrations and Its Applications
Fundamental Theorem of Calculus
Testing Convergence at Endpoints
Section 4.3 – Area and Definite Integrals
8.4 Improper Integrals.
Extreme Values of Functions
Connecting f′ and f″ with the graph of f
Chapter 8 Applications of Definite Integral Section 8.3 Volumes.
Chapter 4 More Derivatives Section 4.1 Chain Rule.
Chapter 5 Integration Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Chapter 8 Section 8.2 Applications of Definite Integral
Integrations and Its Applications
Section 5.3 Definite Integrals and Antiderivatives
Chapter 6 Applications of Derivatives Section 6.5 Trapezoidal Rule.
Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS
Chapter 5 Applications of Derivatives Section 5.6 Related Rates.
Chapter 5 Applications of Derivatives Section 5.6 Related Rates.
Implicit Differentiation
Chapter 2 Limits and Continuity Section 2.3 Continuity.
Chapter 6 The Definite Integral
Connecting f′ and f″ with the graph of f
Rules for Differentiation
Chapter 7 Integration.
Chapter 6 Applications of Derivatives Section 6.2 Definite Integrals.
Chapter 9 Section 9.2 L’Hôpital’s Rule
Chapter 5 Applications of Derivatives Section 5.2 Mean Value Theorem.
Extreme Values of Functions
Derivatives of Exponential and Logarithmic Functions
Definite Integrals & Antiderivatives
Derivatives of Exponential and Logarithmic Functions
Chapter 2 Limits and Continuity Section 2.3 Continuity.
Rates of Change and Limits
Section 5.3 – The Definite Integral
Section 5.3 – The Definite Integral
Chapter 4 More Derivatives Section 4.1 Chain Rule.
Antidifferentiation by Substitution
Antidifferentiation by Parts
Chapter 5 Integration.
Fundamental Theorem of Calculus
Chapter 2 Limits and Continuity Section 2.3 Continuity.
Presentation transcript:

Definite Integrals and Antiderivatives Chapter 6 Applications of Derivatives Section 6.3 Definite Integrals and Antiderivatives

Quick Review

Quick Review Solutions

What you’ll learn about Properties of definite integrals Average value of a function Mean value theorem for definite integrals … and why Working with the properties of definite integrals helps us to understand better the definite integral. Connecting derivatives and definite integrals sets the stage for the Fundamental Theorem of Calculus.

Rules for Definite Integrals

Rules for Definite Integrals

Example Using the Rules for Definite Integrals

Example Using the Rules for Definite Integrals

Example Using the Rules for Definite Integrals

Average (Mean) Value

Example Applying the Definition

The Mean Value Theorem for Definite Integrals

The Mean Value Theorem for Definite Integrals

The Derivative of an Integral

Quick Quiz Sections 6.1 – 6.3

Quick Quiz Sections 6.1 – 6.3

Quick Quiz Sections 6.1 – 6.3

Quick Quiz Sections 6.1 – 6.3

Quick Quiz Sections 6.1 – 6.3

Quick Quiz Sections 6.1 – 6.3

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2024 SlidePlayer.com Inc. All rights reserved.