§4.9 Antiderivatives There are two branches in calculus:

Slides:

Advertisements

Similar presentations

7.1 Antiderivatives OBJECTIVES * Find an antiderivative of a function. *Evaluate indefinite integrals using the basic integration formulas. *Use initial.

Advertisements

In this handout, 4. 7 Antiderivatives 5

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.

Derivative of an Inverse AB Free Response 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 ?

Ch5 Indefinite 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.

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.

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

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.

Math – Antidifferentiation: The Indefinite Integral 1.

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.

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

Lecture III Indefinite integral. Definite integral.

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

5.a – Antiderivatives and The Indefinite Integral.

Section 3.9 Antiderivatives

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

Aim: How to Find the Antiderivative Course: Calculus Do Now: Aim: What is the flip side of the derivative? If f(x) = 3x 2 is the derivative a function,

6.2 Antidifferentiation by Substitution Quick Review.

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

If the following functions represent the derivative of the original function, find the original function. Antiderivative – If F’(x) = f(x) on an interval,

Rules for Integration, Antidifferentiation Section 5.3a.

Algebra and Calculus 8-1 Copyright © Genetic Computer School 2007 Lesson 8 Fundamentals of Calculus.

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

5.4 The Fundamental Theorem of Calculus. I. The Fundamental Theorem of Calculus Part I. A.) If f is a continuous function on [a, b], then the function.

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?

Indefinite Integrals or Antiderivatives

MTH1170 Antiderivatives.

Antiderivatives.

4.4 The Fundamental Theorem of Calculus

4.4 The Fundamental Theorem of Calculus

Antiderivatives 5.1.

Antidifferentiation and Indefinite Integrals

4.4 The Fundamental Theorem of Calculus

Unit 4:Mathematics Introduce various integration functions Aims

Section 4.9: Antiderivatives

6-4 Day 1 Fundamental Theorem of Calculus

The Fundamental Theorems of Calculus

Antiderivatives.

Integration & Area Under a Curve

Applications of Derivatives

Unit 6 – Fundamentals of Calculus Section 6

Calculus for ENGR2130 Lesson 2 Anti-Derivative or Integration

Use the Table of Integrals to evaluate the integral. {image}

Fundamental Theorem of Calculus Indefinite Integrals

For the geometric series below, what is the limit as n →∞ of the ratio of the n + 1 term to the n term?

6.1: Antiderivatives and Indefinite Integrals

Warm Up Before you start pg 342.

AP Calculus November 29-30, 2016 Mrs. Agnew

The Fundamental Theorem of Calculus

Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS

Integration by Substitution (4.5)

Today in Calculus Go over homework Trig Review Mean Value Theorem

The Fundamental Theorems of Calculus

Antiderivatives and Indefinite Integration

Power Series (9.8) March 9th, 2017.

Sec 4.9: Antiderivatives DEFINITION Example A function is called an

1. Antiderivatives and Indefinite Integration

Antidifferentiation by Substitution

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

Antidifferentiation by Parts

Applications of differentiation

Presentation transcript:

§4.9 Antiderivatives There are two branches in calculus: Differential calculus Integral calculus Math 110 (Differential Calculus): Given f(x), find f (x) Applications of derivatives Math 116 (Integral Calculus): Given f(x), find F(x) such that F (x)=f(x), F is called an antiderivative of f Applications of antiderivatives Math 116 is the inverse of Math 110

Def: A function F is called an antiderivative of f on an interval I if F (x) = f(x) for any xI Th: If F is an antiderivative of f on an interval I, then the most general antiderivative of f on I is F(x) + C, where C is an arbitrary constant Note: There are infinitely many antiderivatives for a given f. The difference between them is a constant.

Th: Suppose: (i) f(x)  0 for any x[a,b] (ii) f is continuous on [a,b] then: F(x) (representing the shaded area below and viewed as a function of x ) is an antiderivative of f(x) on [a,b]

Table of antidifferentiation formulas: