Antiderivative: The Indefinite integral

Teacher: Nguyen Thi Le Nhung

3. Practical applications

2. Rules for integrating

common functions

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1. Antiderivative

1. Antiderivative

AntiderivativeDUY TAN UNIVERSITY

A function F(x) for which

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

'( ) ( )F x f x

4 21( ) 1

4F x x x

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

Example 1:

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

Which is called the indefinit integral of f.

( ) ( )f x dx F x C

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.

Fundamental Property of Antiderivative

DUY TAN UNIVERSITY Antiderivative

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for constantkdx kx C k

Section 1: Functions.

2. Rules for integrating

11for all 1

1x dx x C

1

ln | | for all 0dx x C xx

1

for all 0kx kxe dx e C kk

( ) ( ) for constantkf x dx k f x dx C k

[ ( ) ( )] ( ) ( )f x g x dx f x dx g x dx

Section 1 : Functions.DUY TAN UNIVERSITY

3. Practical applicationsExample 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?

2 4 x

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