# Antiderivative: The Indefinite integral - PowerPoint PPT Presentation

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DUY TAN UNIVERSITY. Teacher: Nguyen Thi Le Nhung. Antiderivative: The Indefinite integral. 3. Practical applications. 1. Antiderivative. 2. Rules for integrating common functions. DUY TAN UNIVERSITY. Antiderivative. 1. Antiderivative. A function F ( x ) for which

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Antiderivative: The Indefinite integral

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DUY TAN UNIVERSITY

Teacher: Nguyen Thi Le Nhung

## Antiderivative: The Indefinite integral

3. Practical applications

1. Antiderivative

2. Rules for integrating common functions

DUY TAN UNIVERSITY

### Antiderivative

1. Antiderivative

A function F(x) for which

For every x in the domain of f is said to be an antiderivative of f(x).

Example 1:

Find f(x) such as F(x) is an antidervitative of f(x).

DUY TAN UNIVERSITY

Antiderivative

Fundamental Property of Antiderivative

If F(x) is an antiderivative of the continuous function f(x), any other antiderivative of f(x) has form F(x) +C for some constant C.

We will represent the family of all antiderivatives of f(x) by using the symbolism

Which is called the indefinit integral of f.

### DUY TAN UNIVERSITY

Section 1: Functions.

2. Rules for integrating

DUY TAN UNIVERSITY

### Section 1 : Functions.

3. Practical applications

Example 1

It is estimated that x months from now the population of a certain town will be changing at the rate of people per month. The current population is 3000. What will be the population 4 months from now?

DUY TAN UNIVERSITY

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