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Lesson 3- Definite Integral

# Lesson 3- Definite Integral - ANTIDERIVATIVES(INTEGRAL THE...

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ANTIDERIVATIVES (INTEGRAL)

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THE DEFINITE INTEGRAL define and interpret definite integral, identify and distinguish the different properties of the definite integrals ; and evaluate definite integrals OBJECTIVES:
If F(x) is the integral of f(x)dx , that is, F’(x) = f(x)dx and if a and b are constants, then the definite integral is: ( 29 ] ) a ( F ) b ( F x F dx ) x ( f b a b a - = = where a and b are called lower and upper limits of integration, respectively. The definite integral link the concept of area to other important concepts such as length, volume, density, probability, and other work. HE DEFINITE INTEGRAL

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[ ] b a erval closed the in defined is x f provided dx x f dx x f then b a If b a a b , int ) ( ) ( ) ( , . 1 - = . ) ( ) ( ) ( ), ( int ) ( . 2 exists b f and a f provided dx x f then x f of egral the is x F and b a If b a = OPERTIES OF DEFINITE INTEGRAL [ ] [ ] . 0 ) ( ) ( ) ( ) ( ) ( ) ( , = - = + - + = + = a F a F C a F C a F C x F dx x f is That b a b a
[ ] dx x f dx x f dx x f dx x f x f x f n b a b a b a n ) ( ...... ) ( ) ( ) ( ) .... ( ) ( . 3 2 1 2 1 ± ± = + ± [ ] + = < < b c b a c a dx x f x f dx x f then b c a where b a erval closed the in function continuous

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Lesson 3- Definite Integral - ANTIDERIVATIVES(INTEGRAL THE...

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