4.3 Finding Area Under A Curve Using Area Formulas Objective: Understand Riemann sums, evaluate a definite integral using limits and evaluate using properties.

Slides:



Advertisements
Similar presentations
{ Ch. 5 Review: Integrals AP Calculus. 5.2: The Differential dy 5.2: Linear Approximation 5.3: Indefinite Integrals 5.4: Riemann Sums (Definite Integrals)
Advertisements

5/16/2015 Perkins AP Calculus AB Day 5 Section 4.2.
6.5 The Definite Integral In our definition of net signed area, we assumed that for each positive number n, the Interval [a, b] was subdivided into n subintervals.
Definite Integrals Finding areas using the Fundamental Theorem of Calculus.
5.2 Definite Integrals Quick Review Quick Review Solutions.
Georg Friedrich Bernhard Riemann
4-3 DEFINITE INTEGRALS MS. BATTAGLIA – AP CALCULUS.
Section 7.2a Area between curves.
6.3 Definite Integrals and the Fundamental Theorem.
State Standard – 16.0a Students use definite integrals in problems involving area. Objective – To be able to use the 2 nd derivative test to find concavity.
Section 5.2: Definite Integrals
Areas & Definite Integrals TS: Explicitly assessing information and drawing conclusions.
4-4: The Fundamental Theorems Definition: If f is continuous on [ a,b ] and F is an antiderivative of f on [ a,b ], then: The Fundamental Theorem:
1 Copyright © 2015, 2011 Pearson Education, Inc. Chapter 5 Integration.
Announcements Topics: -sections 7.3 (definite integrals) and 7.4 (FTC) * Read these sections and study solved examples in your textbook! Work On: -Practice.
The Fundamental Theorem of Calculus (4.4) February 4th, 2013.
4.4 The Fundamental Theorem of Calculus
4.4 The Fundamental Theorem of Calculus and The Second Fundamental Theorem of Calculus.
5.4 Fundamental Theorem of Calculus Quick Review.
CHAPTER 4 SECTION 4.3 RIEMANN SUMS AND DEFINITE INTEGRALS.
Chapter 5: The Definite Integral Section 5.2: Definite Integrals
Calculus, 9/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved. MCS 122 Chapter 5 Review.
Section 5.4 Theorems About Definite Integrals. Properties of Limits of Integration If a, b, and c are any numbers and f is a continuous function, then.
CHAPTER Continuity The Definite Integral animation  i=1 n f (x i * )  x f (x) xx Riemann Sum xi*xi* xixi x i+1.
Section 7.4: Arc Length. Arc Length The arch length s of the graph of f(x) over [a,b] is simply the length of the curve.
5.6 Definite Integrals Greg Kelly, Hanford High School, Richland, Washington.
Warm Up 1) 2) 3)Approximate the area under the curve for 0 < t < 40, given by the data, above using a lower Reimann sum with 4 equal subintervals. 4)Approximate.
The Fundamental Theorem of Calculus
Diane Yeoman Definite Integral The Fundamental Theorem.
1 Definite Integrals Section The Definite Integral The definite integral as the area of a region: If f is continuous and non-negative on the closed.
Chapter 5 Integration. Indefinite Integral or Antiderivative.
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.
7.4 Lengths of Curves Quick Review What you’ll learn about A Sine Wave Length of a Smooth Curve Vertical Tangents, Corners, and Cusps Essential Question.
Estimating area under a curve
The Fundamental Theorem of Calculus is appropriately named because it establishes connection between the two branches of calculus: differential calculus.
4.3 Riemann Sums and Definite Integrals. Objectives Understand the definition of a Riemann sum. Evaluate a definite integral using limits. Evaluate a.
Section 4.3 Day 1 Riemann Sums and Definite Integrals AP Calculus BC.
WS: Riemann Sums. TEST TOPICS: Area and Definite Integration Find area under a curve by the limit definition. Given a picture, set up an integral to calculate.
MA Day 30 - February 18, 2013 Section 11.7: Finish optimization examples Section 12.1: Double Integrals over Rectangles.
AP CALCULUS AB CHAPTER 4, SECTION 2(ISH) Area 2013 – 2014 Revised
Lesson 5-2 The Definite Integral. Ice Breaker See handout questions 1 and 2.
Integration/Antiderivative. First let’s talk about what the integral means! Can you list some interpretations of the definite integral?
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.
Chapter 6 Integration Section 5 The Fundamental Theorem of Calculus (Day 1)
4.3 Riemann Sums and Definite Integrals Definition of the Definite Integral If f is defined on the closed interval [a, b] and the limit of a Riemann sum.
“In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used.
Definite Integral df. f continuous function on [a,b]. Divide [a,b] into n equal subintervals of width Let be a sample point. Then the definite integral.
Riemann Sum. Formula Step 1 Step 2 Step 3 Riemann Sum.
Properties of Integrals. Mika Seppälä: Properties of Integrals Basic Properties of Integrals Through this section we assume that all functions are continuous.
5.3 Definite Integrals and Riemann Sums. I. Rules for Definite Integrals.
Announcements Topics: -sections 7.3 (definite integrals) and 7.4 (FTC) * Read these sections and study solved examples in your textbook! Work On: -Practice.
Definite Integrals. Definite Integral is known as a definite integral. It is evaluated using the following formula Otherwise known as the Fundamental.
Section 4.2 The Definite Integral. If f is a continuous function defined for a ≤ x ≤ b, we divide the interval [a, b] into n subintervals of equal width.
5-7: The 1 st Fundamental Theorem & Definite Integrals Objectives: Understand and apply the 1 st Fundamental Theorem ©2003 Roy L. Gover
4.3 Riemann Sums and Definite Integrals
Announcements Topics: -sections 7.3 (definite integrals) and 7.4 (FTC) * Read these sections and study solved examples in your textbook! Work On: -Practice.
5.2 – The Definite Integral. Introduction Recall from the last section: Compute an area Try to find the distance traveled by an object.
DO NOW: v(t) = e sint cost, 0 ≤t≤2∏ (a) Determine when the particle is moving to the right, to the left, and stopped. (b) Find the particles displacement.
5.2/3 Definite Integral and the Fundamental Theorem of Calculus Wed Jan 20 Do Now 1)Find the area under f(x) = 3 – x in the interval [0,3] using 3 leftendpt.
(MTH 250) Lecture 19 Calculus. Previous Lecture’s Summary Definite integrals Fundamental theorem of calculus Mean value theorem for integrals Fundamental.
Chapter 5 AP Calculus BC.
Integration & Area Under a Curve
Section 5.4 Theorems About Definite Integrals
AP Calculus BC October 11, 2016.
4 Integrals.
5.5 Properties of the Definite Integral
Summation Formulas Constant Series.
Integration: Evaluation and Applications
Section 5.2 Definite Integrals
Chapter 5 Integration.
Presentation transcript:

4.3 Finding Area Under A Curve Using Area Formulas Objective: Understand Riemann sums, evaluate a definite integral using limits and evaluate using properties AP Calculus AB

Riemann Sum

Area under the curve between a and b. The integral is equal to the area under the curve only if the curve lies entirely above the x-axis. Theorem 45 on Pg. 274 Today, we are only using formulas for shapes that we know a b

Evaluate Using Formulas 1 3

3 5 (3, 3) (5, 5)

Evaluate Using Formulas -82 (-8, 0) (2, 5)

Evaluate Using Formulas (-3, 0)(0,0)

Evaluate Using Formulas (0, 0) (a, 0) (0, a) (a, 3a)

Formative Assessment Pg (13-32) Answers to Even Problems 24) 8a 26) 4 28) 32

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

© 2024 SlidePlayer.com. Inc. All rights reserved.