Antiderivatives. Indefinite Integral The family of antiderivatives of a function f indicated by The symbol is a stylized S to indicate summation 2.

Slides:

Advertisements

Similar presentations

The Chain Rule Section 3.6c.

Advertisements

DIFFERENTIATION & INTEGRATION CHAPTER 4.  Differentiation is the process of finding the derivative of a function.  Derivative of INTRODUCTION TO DIFFERENTIATION.

Derivatives - Equation of the Tangent Line Now that we can find the slope of the tangent line of a function at a given point, we need to find the equation.

Barnett/Ziegler/Byleen Business Calculus 11e1 Learning Objectives for Section 13.1 Antiderivatives and Indefinite Integrals The student will be able to.

Implicit Differentiation. Objectives Students will be able to Calculate derivative of function defined implicitly. Determine the slope of the tangent.

4.1 Antiderivatives and Indefinite Integrals Defn. A function F(x) is an antiderivative of f(x) on an interval I if F '(x)=f(x) for all x in I. ex. Find.

10.5 Basic Differentiation Properties. Instead of finding the limit of the different quotient to obtain the derivative of a function, we can use the rules.

Every slope is a derivative. Velocity = slope of the tangent line to a position vs. time graph Acceleration = slope of the velocity vs. time graph How.

Formal Definition of Antiderivative and Indefinite Integral Lesson 5-3.

6.1 Antiderivatives and Slope Fields Objectives SWBAT: 1)construct antiderivatives using the fundamental theorem of calculus 2)solve initial value problems.

Copyright © Cengage Learning. All rights reserved.

11 The student will learn about: §4.1 Antiderivatives and Indefinite Integrals. the properties associated with these functions, antiderivatives and indefinite.

Ch5 Indefinite Integral

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Antiderivatives and Slope Fields Section 6.1.

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

Constructing the Antiderivative Solving (Simple) Differential Equations The Fundamental Theorem of Calculus (Part 2) Chapter 6: Calculus~ Hughes-Hallett.

Section 4.1 – Antiderivatives and Indefinite Integration.

Antiderivatives. Antiderivatives Definition A function F is called an antiderivative of f if F ′(x) = f (x) for all x on an interval I. Theorem.

Introduction to Differential Equations. Warmup At each point (x 0,y 0 ) on a function y = f(x), the tangent line has the equation y =2x 0 x - y 0. Find.

Math – Antidifferentiation: The Indefinite Integral 1.

Antiderivatives Lesson 7.1A. Think About It Suppose this is the graph of the derivative of a function What do we know about the original function? Critical.

Barnett/Ziegler/Byleen Business Calculus 11e1 Chapter 13 Review Important Terms, Symbols, Concepts 13.1 Antiderivatives and Indefinite Integrals A function.

The Indefinite Integral

Antiderivatives Indefinite Integrals. Definition  A function F is an antiderivative of f on an interval I if F’(x) = f(x) for all x in I.  Example:

Antiderivatives. Think About It Suppose this is the graph of the derivative of a function What do we know about the original function? Critical numbers.

4.1 ANTIDERIVATIVES & INDEFINITE INTEGRATION. Definition of Antiderivative  A function is an antiderivative of f on an interval I if F’(x) = f(x) for.

4001 ANTIDERIVATIVES AND INDEFINITE INTEGRATION

6.1 Antiderivatives and Indefinite Integration Objectives: 1.) Understand the concept of a antiderivative 2.) Use differentiation rules to produce and.

13.1 Antiderivatives and Indefinite Integrals. The Antiderivative The reverse operation of finding a derivative is called the antiderivative. A function.

Section 1 Antiderivatives and Indefinite Integrals

Antiderivatives and Indefinite Integration. 1. Verify the statement by showing that the derivative of the right side equals the integrand of the left.

4.1 Antiderivatives and Indefinite Integration Definition of Antiderivative: A function F is called an antiderivative of the function f if for every x.

ANTIDERIVATIVES AND INDEFINITE INTEGRATION AB Calculus.

ANTIDERIVATIVES Definition: reverse operation of finding a derivative.

5.a – Antiderivatives and The Indefinite Integral.

Sec. 3.3: Rules of Differentiation. The following rules allow you to find derivatives without the direct use of the limit definition. The Constant Rule.

More with Rules for Differentiation Warm-Up: Find the derivative of f(x) = 3x 2 – 4x 4 +1.

2.1 The Derivative and The Tangent Line Problem Slope of a Tangent Line.

Chapter 6 Integration Section 1 Antiderivatives and Indefinite Integrals.

Chapter 4 Integration 4.1 Antidifferentiation and Indefinate Integrals.

Section 17.4 Integration LAST ONE!!! Yah Buddy!.  A physicist who knows the velocity of a particle might wish to know its position at a given time. 

AP Calculus 3.2 Basic Differentiation Rules Objective: Know and apply the basic rules of differentiation Constant Rule Power Rule Sum and Difference Rule.

Introduction to Integrals Unit 4 Day 1. Do Now  Write a function for which dy / dx = 2 x.  Can you think of more than one?

Inverse Trigonometric Functions: Differentiation & Integration (5. 6/5

MTH1170 Antiderivatives.

AP Calculus BC September 12, 2016.

Antiderivatives.

Antiderivatives 5.1.

Antidifferentiation and Indefinite Integrals

MTH1170 Implicit Differentiation

Section 4.1 – Antiderivatives and Indefinite Integration

§4.9 Antiderivatives There are two branches in calculus:

Calculus for ENGR2130 Lesson 2 Anti-Derivative or Integration

Section 6.1 Slope Fields.

The Natural Logarithmic Function: Integration (Section 5-2)

6.1: Antiderivatives and Indefinite Integrals

Antiderivatives Lesson 7.1A.

Antiderivatives.

The Indefinite Integral

Section 2 – Derivatives and Antiderivatives

5.1 Integrals Rita Korsunsky.

1. Antiderivatives and Indefinite Integration

Slope Fields (6.1) January 10th, 2017.

Objectives To be able to find a specific function when given the derivative and a known location.

More with Rules for Differentiation

1. Determine 2. At what point of the curve y=cosh x does the tangent have slope 1? 3. Find the value of the expression by interpreting.

Chapter 5 Integration Section R Review.

2.5 Basic Differentiation Properties

Section 1 Antiderivatives and Indefinite Integrals

Presentation transcript:

Antiderivatives

Indefinite Integral The family of antiderivatives of a function f indicated by The symbol is a stylized S to indicate summation 2

Indefinite Integral The indefinite integral is a family of functions The + C represents an arbitrary constant The constant of integration 3

Properties of Indefinite Integrals The power rule The integral of a sum (difference) is the sum (difference) of the integrals 4

Properties of Indefinite Integrals The derivative of the indefinite integral is the original function A constant can be factored out of the integral 5

Example : Evaluate

Examples Determine the indefinite integrals as specified below 7

Integrate

Find each antiderivative

Solve the differential equation

Given that the graph of f(x) passes through the point (1,6) and that the slope of its tangent line at (x.f(x) is 2x+1, find f(6)