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Lesson 16  Antiderivatives
1
Lesson 16
Antiderivatives
So far in this course, we have been interested in finding derivatives and in the applications of
derivatives.
In this chapter, we will look at the reverse process.
Here we will be given the “answer”
and we’ll have to find the “problem.”
This process is generally called
integration
.
We can use integration to solve a variety of problems.
Antiderivatives
A function
F
is an antiderivative of
f
on interval
I
if
( )
( )
F x
f x
′
=
for all
x
in
I.
The process of finding an antiderivative is called
antidifferentiation
or
finding an indefinite
integral
.
Example 1:
Suppose
.
27
)
(
and
10
)
(
3
3

=
+
=
x
x
K
x
x
H
If
2
3
)
(
x
x
f
=
, show that each of
H
and
K
is an antiderivative of
f
, and draw a conclusion.
Notation
:
We will use the integral sign
∫
to indicate integration (antidifferentiation).
Problems will
be written in the form
∫
+
=
.
)
(
)
(
C
x
F
dx
x
f
This indicates that the indefinite integral of
)
(
x
f
with
respect to the variable
x
is
C
x
F
+
)
(
where
)
(
x
F
is an antiderivative of
f.
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 Fall '08
 CONSTANTE
 Antiderivatives, Derivative

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