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Company LOGO Module 5.1: Antiderivative - The Indefinite integral Duy Tân University Lecturer: Nguyen Thi Ngoc Bich Natural Science Department Chapter.

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Presentation on theme: "Company LOGO Module 5.1: Antiderivative - The Indefinite integral Duy Tân University Lecturer: Nguyen Thi Ngoc Bich Natural Science Department Chapter."— Presentation transcript:

1 Company LOGO Module 5.1: Antiderivative - The Indefinite integral Duy Tân University Lecturer: Nguyen Thi Ngoc Bich Natural Science Department Chapter 5: Integration Module 5.1. Antiderivetive – The indefinite integral

2 Company LOGO Natural Science Department Chapter 5: Integration Module 5.1. Antiderivetive – The indefinite integral 2 5.1 Antiderivative - The Indefinite integral 1.Antiderivative 2. Rules for integrating 3. Practical applications

3 Company LOGO Natural Science Department Chapter 5: Integration Module 5.1. Antiderivetive – The indefinite integral 1. Antiderivative - Antiderivative: A function F(x) for which for every x in the domain of f is said to be an antiderivative of f(x). - Fundamental Property of Antiderivative: If F(x) is an antiderivative of the continuous function f(x), then any other antiderivative of f(x) has the form G(x) = F(x) + C, for some constant C.

4 Company LOGO Natural Science Department Chapter 5: Integration Module 5.1. Antiderivetive – The indefinite integral 1. Antiderivative We will represent the family of all antiderivatives of f(x) by using the symbolism: which is called the indefinite integral of f

5 Company LOGO Natural Science Department Chapter 5: Integration Module 5.1. Antiderivetive – The indefinite integral 2. Rules for integrating + Rules for integrating common functions: + Algebraic rules for indefinite integration:

6 Company LOGO Natural Science Department Chapter 5: Integration Module 5.1. Antiderivetive – The indefinite integral 3. Practical applications Example 1: It is estimated that x months from now the polulation of a certain town will be changing at the rate of people per month. The current population is 5000. What will be the population 9 months from now ? Example 2: A manufacturer has found that marginal cost is dollars per unit when q units have produced.The total cost of producing the first 2 units is $ 900. What is the total cost of producing the first 5 units ?

7 Company LOGO Natural Science Department Chapter 5: Integration Module 5.1. Antiderivetive – The indefinite integral ; Natural Science Department

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