Objective:To use the Fundamental Theorem of Calculus to evaluate definite integrals of polynomial functions. To find indefinite integrals of polynomial.

Slides:

Advertisements

Similar presentations

6 Integration Antiderivatives and the Rules of Integration

Advertisements

Copyright © 2008 Pearson Education, Inc. Chapter 7 Integration Copyright © 2008 Pearson Education, Inc.

CHAPTER 4 THE DEFINITE INTEGRAL.

Areas and Definite Integrals. Objectives Students will be able to Calculate a definite integral. Calculate the area between a curve and the x-axis over.

Section 4.3 Indefinite Integrals and Net Change Theorem Math 1231: Single-Variable Calculus.

Section 4.3 Fundamental Theorem of Calculus Math 1231: Single-Variable Calculus.

The Fundamental Theorem of Calculus Inverse Operations.

Example We can also evaluate a definite integral by interpretation of definite integral. Ex. Find by interpretation of definite integral. Sol. By the interpretation.

1 5.4 – Indefinite Integrals and The Net Change Theorem.

5.4 The Fundamental Theorem. The Fundamental Theorem of Calculus, Part 1 If f is continuous on, then the function has a derivative at every point in,

4-3 DEFINITE INTEGRALS MS. BATTAGLIA – AP CALCULUS.

Section 5.3 – The Definite Integral

Section 5.3: Evaluating Definite Integrals Practice HW from Stewart Textbook (not to hand in) p. 374 # 1-27 odd, odd.

Question from Test 1 Liquid drains into a tank at the rate 21e-3t units per minute. If the tank starts empty and can hold 6 units, at what time will it.

The Fundamental Theorem of Calculus Lesson Definite Integral Recall that the definite integral was defined as But … finding the limit is not often.

5.c – The Fundamental Theorem of Calculus and Definite Integrals.

4.4c 2nd Fundamental Theorem of Calculus. Second Fundamental Theorem: 1. Derivative of an integral.

7.4: The Fundamental Theorem of Calculus Objectives: To use the FTC to evaluate definite integrals To calculate total area under a curve using FTC and.

The Trapezoidal Rule Some elementary functions simply do not have antiderivatives that are elementary functions. For example, there is no elementary function.

Antiderivatives An antiderivative of f(x) is any function F(x) such that F’(x) = f(x)

Areas & Definite Integrals TS: Explicitly assessing information and drawing conclusions.

CHAPTER 4 SECTION 4.4 THE FUNDAMENTAL THEOREM OF CALCULUS.

5.4 Fundamental Theorem of Calculus. It is difficult to overestimate the power of the equation: It says that every continuous function f is the derivative.

Section 4.4 The Fundamental Theorem of Calculus Part II – The Second Fundamental Theorem.

The Fundamental Theorem of Calculus (4.4) February 4th, 2013.

The Fundamental Theorems of Calculus Lesson 5.4. First Fundamental Theorem of Calculus Given f is  continuous on interval [a, b]  F is any function.

4.4 The Fundamental Theorem of Calculus

Integration 4 Copyright © Cengage Learning. All rights reserved.

Lecture 18 More on the Fundamental Theorem of Calculus.

4-4 THE FUNDAMENTAL THEOREM OF CALCULUS MS. BATTAGLIA – AP CALCULUS.

F UNDAMENTAL T HEOREM OF CALCULUS 4-B. Fundamental Theorem of Calculus If f(x) is continuous at every point [a, b] And F(x) is the antiderivative of f(x)

4009 Fundamental Theorem of Calculus (Part 2) BC CALCULUS.

SECTION 5.4 The Fundamental Theorem of Calculus. Basically, (definite) integration and differentiation are inverse operations.

5.4 Fundamental Theorem of Calculus Quick Review.

Mathematics. Session Definite Integrals –1 Session Objectives  Fundamental Theorem of Integral Calculus  Evaluation of Definite Integrals by Substitution.

SPECIALIST MATHS Calculus Week 6 Definite Integrals & Areas.

Section 4.2 Definite Integral Math 1231: Single-Variable Calculus.

FTC Review; The Method of Substitution

The Fundamental Theorem of Calculus

Current circulation is 3000 per month. Growth rate is C’(t)=. Find C(t). C(t) = C(0) = c = C(t) =

Chapter 5 Integration. Indefinite Integral or Antiderivative.

4.4 The Fundamental Theorem of Calculus. Essential Question: How are the integral & the derivative related?

Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1 Section 6.4 Fundamental Theorem of Calculus Applications of Derivatives Chapter 6.

Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 4.8 Antiderivatives.

5.3 – The Fundamental Theorem of Calculus

4032 Fundamental Theorem AP Calculus. Where we have come. Calculus I: Rate of Change Function.

Fundamental Theorem AP Calculus. Where we have come. Calculus I: Rate of Change Function.

5.3 Definite Integrals and Antiderivatives. What you’ll learn about Properties of Definite Integrals Average Value of a Function Mean Value Theorem for.

AP Calculus Mrs. Mongold. The Fundamental Theorem of Calculus, Part 1 If f is continuous on, then the function has a derivative at every point in, and.

The Fundamental Theorem of Calculus is appropriately named because it establishes connection between the two branches of calculus: differential calculus.

Chapter 6 Integration Section 5 The Fundamental Theorem of Calculus (Day 1)

CHAPTER Continuity Fundamental Theorem of Calculus In this lecture you will learn the most important relation between derivatives and areas (definite.

5.3 Definite Integrals and Riemann Sums. I. Rules for Definite Integrals.

5-7: The 1 st Fundamental Theorem & Definite Integrals Objectives: Understand and apply the 1 st Fundamental Theorem ©2003 Roy L. Gover

Essential Question: How is a definite integral related to area ?

Chapter 6 The Definite Integral. There are two fundamental problems of calculus 1.Finding the slope of a curve at a point 2.Finding the area of a region.

THE FUNDAMENTAL THEOREM OF CALCULUS Section 4.4. THE FUNDAMENTAL THEOREM OF CALCULUS Informally, the theorem states that differentiation and definite.

The Fundamental Theorem of Calculus is appropriately named because it establishes connection between the two branches of calculus: differential calculus.

6 Integration Antiderivatives and the Rules of Integration

MTH1170 The Fundamental Theorem of Calculus

4.4 The Fundamental Theorem of Calculus

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. {image}

The Fundamental Theorems of Calculus

Unit 6 – Fundamentals of Calculus Section 6

Section 4.3 – Area and Definite Integrals

Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS

§ 6.3 Definite Integrals and the Fundamental Theorem.

Chapter 7 Integration.

§ 6.3 Definite Integrals and the Fundamental Theorem.

5.1 Integrals Rita Korsunsky.

Presentation transcript:

Objective:To use the Fundamental Theorem of Calculus to evaluate definite integrals of polynomial functions. To find indefinite integrals of polynomial functions

If a function is continuous on the closed interval [a, b], then

» Evaluate Find the antiderivative Evaluate for 4 and 2

» Evaluate

» Find the area of the shaded region.

» Part of the advertisement on a billboard contains a parabola that can be modeled by », where x and y are in feet. If they » need to paint 6 feet across of the parabola to the bottom of the billboard with the parabola centered horizontally, how much of the sign do they need to paint?