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Math 121 Lecture 29
Derivatives:
Definition.
Techniques.
Applications.

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*Sign up* !
Antidifferentiation
!
Areas and Riemann Sums
!
Definite Integrals and the Fundamental Theorem
!
Areas in the
xy
-Plane
!
Applications of the Definite Integral
§ 6.1
Antidifferentiation

!
Antidifferentiation
!
Finding Antiderivatives
!
Theorems of Antidifferentiation
!
The Indefinite Integral
!
Rules of Integration
!
Antiderivatives in Application
Definition
Example
Antidifferentiation
:
The process of
determining
f
(
x
) given
f
!
(
x
)
If
, then

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*Sign up* Find all antiderivatives of the
given
function.
The derivative of
x
9
is exactly 9
x
8
.
Therefore,
x
9
is an
antiderivative of 9
x
8
.
So is
x
9
+ 5 and
x
9
-17.2.
It turns out
that all antiderivatives of
f
(
x
) are of the form
x
9
+
C
(where
C
is any constant) as we will see next.

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*Sign up* Determine the following.
Using the rules of indefinite integrals, we have
Find the function
f
(
x
) for which
and
f
(1) = 3.
The unknown function

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