Presentation is loading. Please wait.

Presentation is loading. Please wait.

Chapter 5 The Definite Integral. Chapter 5 The Definite Integral.

Published byAnabel Roberts Modified over 6 years ago

Similar presentations

Presentation on theme: "Chapter 5 The Definite Integral. Chapter 5 The Definite Integral."— Presentation transcript:

1

2 Chapter 5 The Definite Integral

3 Quick Review

4 Quick Review Solutions

5 5.2 Definite Integrals

6 What you’ll learn about
Riemann Sums The Definite Integral Computing Definite Integrals on a Calculator Integrability … and why The definite integral is the basis of integral calculus, just as the derivative is the basis of differential calculus.

7 Sigma Notation

8 The Definite Integral as a Limit of Riemann Sums

9 The Existence of Definite Integrals

10 The Definite Integral of a Continuous Function on [a,b]

11 The Definite Integral

12 Example Using the Notation

13 Area Under a Curve (as a Definite Integral)

14 Area

15 The Integral of a Constant

16 Example Using fnInt TI TI 84 TI-nspire

Download ppt "Chapter 5 The Definite Integral. Chapter 5 The Definite Integral."

Similar presentations

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Definite Integrals Section 5.2.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Definite Integrals Section 5.2.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 1.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 1.
5.2 Definite Integrals Quick Review Quick Review Solutions.

5.2 Definite Integrals Quick Review Quick Review Solutions.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 1.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 5- 1.
M 112 Short Course in Calculus Chapter 5 – Accumulated Change: The Definite Integral Sections 5.2 – The Definite Integral V. J. Motto.

M 112 Short Course in Calculus Chapter 5 – Accumulated Change: The Definite Integral Sections 5.2 – The Definite Integral V. J. Motto.
3.3 Rules for Differentiation. What you’ll learn about Positive Integer Powers, Multiples, Sums and Differences Products and Quotients Negative Integer.

3.3 Rules for Differentiation. What you’ll learn about Positive Integer Powers, Multiples, Sums and Differences Products and Quotients Negative Integer.
5.4 Fundamental Theorem of Calculus Quick Review.

5.4 Fundamental Theorem of Calculus Quick Review.
Chapter 5: The Definite Integral Section 5.2: Definite Integrals

Chapter 5: The Definite Integral Section 5.2: Definite Integrals
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 5.1 Estimating with Finite Sums.
In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules.

In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules.
Chapter 5 – The Definite Integral. 5.1 Estimating with Finite Sums Example Finding Distance Traveled when Velocity Varies.

Chapter 5 – The Definite Integral. 5.1 Estimating with Finite Sums Example Finding Distance Traveled when Velocity Varies.
Section 5.2 The Definite Integral Calculus Winter, 2013.

Section 5.2 The Definite Integral Calculus Winter, 2013.
Sigma Notations Example This tells us to start with k=1 This tells us to end with k=100 This tells us to add. Formula.

Sigma Notations Example This tells us to start with k=1 This tells us to end with k=100 This tells us to add. Formula.
Riemann Sums and Definite Integration y = 6 y = x ex: Estimate the area under the curve y = x 2 + 2 from x = 0 to 3 using 3 subintervals and right endpoints,

Riemann Sums and Definite Integration y = 6 y = x ex: Estimate the area under the curve y = x from x = 0 to 3 using 3 subintervals and right endpoints,
In this section, we will begin to look at Σ notation and how it can be used to represent Riemann sums (rectangle approximations) of definite integrals.

In this section, we will begin to look at Σ notation and how it can be used to represent Riemann sums (rectangle approximations) of definite integrals.
5.2 Definite Integrals Objectives SWBAT: 1) express the area under a curve as a definite integral and as a limit of Riemann sums 2) compute the area under.

5.2 Definite Integrals Objectives SWBAT: 1) express the area under a curve as a definite integral and as a limit of Riemann sums 2) compute the area under.
MTH 252 Integral Calculus Chapter 6 – Integration Section 6.6 – The Fundamental Theorem of Calculus Copyright © 2005 by Ron Wallace, all rights reserved.

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.

The Fundamental Theorem of Calculus is appropriately named because it establishes connection between the two branches of calculus: differential calculus.
Fundamental Theorem of Calculus: Makes a connection between Indefinite Integrals (Antiderivatives) and Definite Integrals (“Area”) Historically, indefinite.

Fundamental Theorem of Calculus: Makes a connection between Indefinite Integrals (Antiderivatives) and Definite Integrals (“Area”) Historically, indefinite.
Rules for Differentiation

Rules for Differentiation

Similar presentations

Ads by Google