Section 4.9ANTIDERIVATES

DEFINITION: A Function F is called the antiderivative of on an interval I if

Theorem: If F is an antiderivative of on an interval, then the most general antiderivative of is F(x) + C ,

where C is an arbitrary constant.

f'( ) ( )F x f x

f

f

GENERAL ANTIDERIVATIVE:

1

( ) , 1

( )1

n

n

f x x n

is

xF x C

n

FUNCTION PARTICULAR ANTIDERIVTIVE

cf(x) cF(x)

f(x)+g(x) F(x)+G(x)

1/x

cosx sinx

sinx -cosx

secxtanx secx

ln xxe xe

PRACTICE PROBLEMS

2

3 22

3

3

1. '( ) 3 2

12. '( ) 2

2

3. '( ) cos 2sin 3

1 34. '( )

5. "( ) 3 4

6. "( ) 4 6 40 , (0) 2, '(0) 1

7. "( ) sin cos , (0) 3, '(0) 4

x

f x x

f x x

f x x x e

f x xx x

f x x x

f x x x f f

f x x x f f