Presentation is loading. Please wait.

Presentation is loading. Please wait.

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

Published byJohn Byrd Modified over 9 years ago

Similar presentations

Presentation on theme: "4.1 Antiderivatives and Indefinite Integration Definition of Antiderivative: A function F is called an antiderivative of the function f if for every x."— Presentation transcript:

1 4.1 Antiderivatives and Indefinite Integration Definition of Antiderivative: A function F is called an antiderivative of the function f if for every x in the domain of f F’(x) = f(x) so, dy = f(x) dx Integration is denoted by an integral sign. IntegrandVariable of Integration Constant of Integration F’(x) also = f(x) (first derivative)

2 Basic Integration Formulas

3 Integrate

4 Rewriting before integrating

5 Find the general solution of the equation F’(x) = and find the particular solution given the point F(1) = 0. Now plug in (1,0) and solve for C. 0 = -1 + C C = 1 Final answer.

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

Similar presentations

6.2 Antidifferentiation by Substitution

6.2 Antidifferentiation by Substitution
Sec. 4.5: Integration by Substitution. T HEOREM 4.12 Antidifferentiation of a Composite Function Let g be a function whose range is an interval I, and.

Sec. 4.5: Integration by Substitution. T HEOREM 4.12 Antidifferentiation of a Composite Function Let g be a function whose range is an interval I, and.
Antiderivatives (7.4, 8.2, 10.1) JMerrill, 2009. Review Info - Antiderivatives General solutions: Integrand Variable of Integration Constant of Integration.

Antiderivatives (7.4, 8.2, 10.1) JMerrill, Review Info - Antiderivatives General solutions: Integrand Variable of Integration Constant of Integration.
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.

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.
Warm Up. 7.4 A – Separable Differential Equations Use separation and initial values to solve differential equations.

Warm Up. 7.4 A – Separable Differential Equations Use separation and initial values to solve differential equations.
1Chapter 2. 2 Example 3Chapter 2 4 EXAMPLE 5Chapter 2.

1Chapter 2. 2 Example 3Chapter 2 4 EXAMPLE 5Chapter 2.
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 ?

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. Antiderivatives and Indefinite Integration.

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

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.

Copyright © Cengage Learning. All rights reserved.
4.1 The Indefinite Integral. Antiderivative An antiderivative of a function f is a function F such that Ex.An antiderivative of since is.

4.1 The Indefinite Integral. Antiderivative An antiderivative of a function f is a function F such that Ex.An antiderivative of since is.
 Constructing the Antiderivative  Solving (Simple) Differential Equations  The Fundamental Theorem of Calculus (Part 2) Chapter 6: Calculus~ Hughes-

 Constructing the Antiderivative  Solving (Simple) Differential Equations  The Fundamental Theorem of Calculus (Part 2) Chapter 6: Calculus~ Hughes-
3.1 Definition of the Derivative & Graphing the Derivative

3.1 Definition of the Derivative & Graphing the Derivative
Remember that given a position function we can find the velocity by evaluating the derivative of the position function with respect to time at the particular.

Remember that given a position function we can find the velocity by evaluating the derivative of the position function with respect to time at the particular.
MAT 1221 survey of Calculus Section 6.1 Antiderivatives and Indefinite Integrals

MAT 1221 survey of Calculus Section 6.1 Antiderivatives and Indefinite Integrals
The Indefinite Integral

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 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:
Dr. Omar Al Jadaan Assistant Professor – Computer Science & Mathematics General Education Department Mathematics.

Dr. Omar Al Jadaan Assistant Professor – Computer Science & Mathematics General Education Department Mathematics.
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.

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.

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.

Similar presentations

Ads by Google