Antiderivatives. Mr. Baird knows the velocity of particle and wants to know its position at a given time Ms. Bertsos knows the rate a population of bacteria.

Slides:

Advertisements

Similar presentations

Indefinite Integrals 6.1. Integration - Antidifferentiation - method of solution to a differential equation INdefinite Integral Integration Symbol Variable.

Advertisements

Indefinite Integrals. Objectives Students will be able to Calculate an indefinite integral. Calculate a definite integral.

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.

Antidifferentiation TS: Making decisions after reflection and review.

Chapter 6 The Integral Sections 6.1, 6.2, and 6.3

Antiderivatives Definition A function F(x) is called an antiderivative of f(x) if F ′(x) = f (x). Examples: What’s the antiderivative of f(x) = 1/x ?

Integration. Indefinite Integral Suppose we know that a graph has gradient –2, what is the equation of the graph? There are many possible equations for.

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

The Integral chapter 5 The Indefinite Integral Substitution The Definite Integral As a Sum The Definite Integral As Area The Definite Integral: The Fundamental.

INTEGRATION ANTIDERIVATIVE: If F ' ( x ) = f ( x ), then F ( x ) is an antiderivative of f ( x ). If F ( x ) and G ( x ) are both antiderivatives of a.

Integrals 5. Evaluating Definite Integrals Evaluating Definite Integrals We have computed integrals from the definition as a limit of Riemann sums.

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

Section 4.1 – Antiderivatives and Indefinite Integration.

Antiderivatives: Think “undoing” derivatives Since: We say is the “antiderivative of.

4.1 The Indefinite Integral. Antiderivative An antiderivative of a function f is a function F such that Ex.An antiderivative of since is.

MAT 1221 survey of Calculus Section 6.1 Antiderivatives and Indefinite Integrals

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.

Lesson 15-2 part 3 Antiderivatives and the Rules of Integration Objective: To find the antiderivatives (integrals) of polynomial functions.

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.

Sect. 4.1 Antiderivatives Sect. 4.2 Area Sect. 4.3 Riemann Sums/Definite Integrals Sect. 4.4 FTC and Average Value Sect. 4.5 Integration by Substitution.

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.

Antidifferentiation: The Indefinite Intergral Chapter Five.

4001 ANTIDERIVATIVES AND INDEFINITE INTEGRATION

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

Math – Antiderivatives 1. Sometimes we know the derivative of a function, and want to find the original function. (ex: finding displacement from.

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.

Lecture III Indefinite integral. Definite integral.

1 § 12.1 Antiderivatives and Indefinite Integrals The student will learn about: antiderivatives, indefinite integrals, and applications.

Write the derivative for each of the following.. Calculus Indefinite Integrals Tuesday, December 15, 2015 (with a hint of the definite integral)

ANTIDERIVATIVES AND INDEFINITE INTEGRATION AB Calculus.

5.a – Antiderivatives and The Indefinite Integral.

Distance Traveled Area Under a curve Antiderivatives

BY DR. SAFA AHMED ELASKARY FACULTY OF ALLIED MEDICAL OF SCIENCES Lecture (1) Antiderivatives and the Rules of Integration.

January 25th, 2013 Antiderivatives & Indefinite Integration (4.1)

Substitution Lesson 7.2. Review Recall the chain rule for derivatives We can use the concept in reverse To find the antiderivatives or integrals of complicated.

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

Chapter 4 Integration 4.1 Antidifferentiation and Indefinate Integrals.

Antiderivatives and Indefinite Integrals Modified by Mrs. King from Paul's Online Math Tutorials and Notes

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. 

Indefinite Integrals or Antiderivatives

MTH1170 Antiderivatives.

Antiderivatives 5.1.

Antidifferentiation and Indefinite Integrals

Integration in physics.

6 Integration Antiderivatives and the Rules of Integration

MTH1170 The Fundamental Theorem of Calculus

Copyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc.

Section 4.1 – Antiderivatives and Indefinite Integration

Antiderivatives Chapter 4.9

Antiderivatives.

and Indefinite Integration (Part I)

4.1 Antiderivatives and Indefinite Integration

The Fundamental Theorem of Calculus (FTC)

Section Indefinite Integrals

Chapter 4 Integration.

6.1: Antiderivatives and Indefinite Integrals

Antiderivatives & Indefinite Integration

Antiderivatives.

Chapter 7 Integration.

The Indefinite Integral

Substitution Lesson 7.2.

Section Indefinite Integrals

The Indefinite Integral

1. Antiderivatives and Indefinite Integration

Calculus I (MAT 145) Dr. Day Monday April 15, 2019

Presentation transcript:

Antiderivatives

Mr. Baird knows the velocity of particle and wants to know its position at a given time Ms. Bertsos knows the rate a population of bacteria is increasing and she wants to know what the size of the population will be at a future time. In each case the rate of change (the derivative) is known….but what is the original function? The original function is called the ANTIDERIVATIVE ANTIDERIVATIVE of the rate of change.

A function is called an antiderivative of on an interval if for all x in. DEFINITION

Suppose What is its antiderivative? We can make some guesses They all fit!

Theorem If is an antiderivative of on an interval, then the most general antiderivative of on is where is an arbitrary constant.

Finding an antiderivative is also known as Indefinite Integration and the Antiderivative is the Indefinite Integral (Especially for us old guys!) And the symbol for integration is an elongated S More on why it’s an S later!

Integrand Variable of Integration Constant of Integration This is read: The antiderivative of f with respect to x or the indefinite integral of f with respect to x is equal to…..

What is the Antiderivative of Derivative We “kinda” multiply Take the integral of both sides We know what to differentiate to get

Some General Rules They are just the derivative rules in reverse Differentiation Formula Integration Formula “Pulling out a konstant”

Some General Rules Differentiation Formula Integration Formula Sum / Difference Rule for Integrals Power Rule for Integrals

Some General Rules Differentiation Formula Integration Formula All the other trig functions follow