Antiderivatives

Jul 22, 2012

70 likes | 330 Views

Mika Sepp?l?: Antiderivatives. Antiderivative. Definition. A function F is an antiderivative of a function f if F'=f.. Theorem. Assume that f is continuous on an interval (a,b). If F1 and F2 are both antiderivatives of the function f on the interval (a,b), then there is a constant C

Share Presentation

Embed Code

Link

reegan

Download Presentation

Antiderivatives

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

1. Antiderivatives Definition of AntiderivativesTable of AntiderivativesRole of the Additive ConstantAntiderivatives GraphicallySlope Fields

2. Mika Sepp�l�: Antiderivatives Antiderivative

ANTIDERIVATIVES AND INDEFINITE INTEGRATION

When you are done with your homework, you should be able to. Write the general solution of a differential equationUse indefinite integral notation for antiderivativesUse basic integration rules to find antiderivativesFind a particular solution of a differential equation. Thales lived in 600 BC.

449 views • 16 slides

Antiderivatives

Antiderivatives. 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.

1.7k views • 11 slides

Antiderivatives and Indefinite Integrals

Antiderivatives and Indefinite Integrals. Modified by Mrs. King from Paul's Online Math Tutorials and Notes http://tutorial.math.lamar.edu/AllBrowsers/2413/ IndefiniteIntegrals.asp. Introduction.

353 views • 14 slides

Antiderivatives

Antiderivatives. Section 6.1. Consider:. or. then:. Given:. find. First, a little review:. It doesn’t matter whether the constant was 3 or -5, since when we take the derivative the constant disappears. However, when we try to reverse the operation:.

270 views • 10 slides

D4 - Antiderivatives

D4 - Antiderivatives. IB Math HL/SL. (A) Review. To date, what we have presented are differentiation techniques (power rule, sum/diff rule, product rule, quotient rule, chain rule)

515 views • 14 slides

Section 4.8 - Antiderivatives

Section 4.8 - Antiderivatives. If the following functions represent the derivative of the original function, find the original function. Antiderivative – If F’(x) = f(x) on an interval, then F(x) is the antiderivative of f(x) for every value of x on the interval. .

394 views • 16 slides

Section 15.1 - Antiderivatives

Section 15.1 - Antiderivatives. 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 ? What’s the antiderivative of g(x) = 2x ? What’s the antiderivative of h(x) = 4 ?.

281 views • 9 slides

ANTIDERIVATIVES AND INDEFINITE INTEGRATION

ANTIDERIVATIVES AND INDEFINITE INTEGRATION. AB Calculus. ANTIDERIVATIVES AND INDEFINITE INTEGRATION. Rem: DEFN : A function F is called an Antiderivative of the function f , if for every x in f : F / (x) = f(x)

793 views • 24 slides

Antiderivatives

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: F(x) = x 3 when f(x) = 3x 2 In other words, we are going backwards – given the derivative, what was the original function?.

551 views • 23 slides

4 .9 Antiderivatives

4 .9 Antiderivatives. 1. Definition :. F(x) is an antiderivative. of f(x) if F′(x)=f(x). 2. Example :. f (x)=x 3 +2x. F 1 (x)=. F 2 (x)=. F (x)=. 3. Theorem :. If F(x) is an antiderivative. of f(x), then so is F(x)+C. Antiderivative. x n+1. ———+ C. n+1. sin(x).

313 views • 15 slides

Antiderivatives (7.4, 8.2, 10.1)

Antiderivatives (7.4, 8.2, 10.1). JMerrill, 2009. Review Info - Antiderivatives. General solutions:. Variable of Integration. Constant of Integration. Integrand. Review. Rewriting & Integrating – general solution. Particular Solutions.

435 views • 33 slides

Antiderivatives – Basic, Substitution, Bounded

Antiderivatives – Basic, Substitution, Bounded. Unit 8. Welcome Assignment – 8/27/12. For your first warm up, please copy the following notes into your notebook: Antiderivatives The inverse operation of differentiation

323 views • 19 slides

7.1: Antiderivatives

DERIVATIVES. 7.1: Antiderivatives. Objectives: To find the antiderivative of a function using the rules of antidifferentiation To find the indefinite integral To apply the indefinite integral. Up until this point, we have done problems such as: f(x)= 2x +7, find f’(x)

838 views • 19 slides

Antiderivatives

Antiderivatives. Indefinite Integral. The family of antiderivatives of a function f indicated by The symbol is a stylized S to indicate summation. Indefinite Integral. The indefinite integral is a family of functions The + C represents an arbitrary constant

551 views • 19 slides

4.1A Antiderivatives

4.1A Antiderivatives. A function F is the Antiderivative of f if F  ( x ) = f ( x ) for all x. Ex 1 : Find the Antiderivative:. Power Rule:. NOTE: see pg. 250 for more Antiderivative Rules. Ex 2 : Find all functions g such that:. Ex 3 : Evaluate. Ex 4 : Evaluate. y.

302 views • 19 slides

Section 4.9 Antiderivatives

Applications of Differentiation. Section 4.9 Antiderivatives. Introduction. A physicist who knows the velocity of a particle might wish to know its position at a given time.

940 views • 66 slides

Antiderivatives

Antiderivatives. 5.1. Discovery of Power Rule for Antiderivatives. If f ‘ (x) = Then f(x) =. If f ‘ (x) = Then f(x) =. If f ‘ (x) = Then f(x) =. If f ‘ (x) = Then f(x) =. Differentiation. Integration. The process of finding a derivative. The process of finding the antiderivative.

175 views • 15 slides

ANTIDERIVATIVES AND INDEFINITE INTEGRATION

ANTIDERIVATIVES AND INDEFINITE INTEGRATION. Section 4.1. When you are done with your homework, you should be able to…. Write the general solution of a differential equation Use indefinite integral notation for antiderivatives Use basic integration rules to find antiderivatives

193 views • 16 slides

More Related