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Example Questions
Example Question #2 : Fundamental Theorem Of Calculus
Evaluate when
.
Via the Fundamental Theorem of Calculus, we know that, given a function ,
. Therefore,
.
Example Question #1 : Fundamental Theorem Of Calculus
Evaluate when
.
Via the Fundamental Theorem of Calculus, we know that, given a function ,
. Therefore,
.
Example Question #2 : Fundamental Theorem Of Calculus
Suppose we have the function
What is the derivative, ?
We can view the function as a function of
, as so
where .
We can find the derivative of using the chain rule:
where can be found using the fundamental theorem of calculus:
So we get
Example Question #1 : Fundamental Theorem Of Calculus
If , what is
?
By the Fundamental Theorem of Calculus, we know that given a function,
.
Thus,
Example Question #1 : Fundamental Theorem Of Calculus
If , what is
?
By the Fundamental Theorem of Calculus, we know that given a function,
.
Thus,
Example Question #2 : Fundamental Theorem Of Calculus
If , what is
?
By the Fundamental Theorem of Calculus, we know that given a function,
.
Thus,
Example Question #1901 : Calculus Ii
Given
, what is
?
None of the above.
By the Fundamental Theorem of Calculus, for all functions that are continuously defined on the interval
with
in
and for all functions
defined by by
, we know that
.
Thus, for
,
.
Therefore,
Example Question #4 : Fundamental Theorem Of Calculus And Techniques Of Antidifferentiation
Given
, what is
?
None of the above.
By the Fundamental Theorem of Calculus, for all functions that are continuously defined on the interval
with
in
and for all functions
defined by by
, we know that
.
Given
, then
.
Therefore,
.
Example Question #11 : Fundamental Theorem Of Calculus
Given
, what is
?
By the Fundamental Theorem of Calculus, for all functions that are continuously defined on the interval
with
in
and for all functions
defined by by
, we know that
.
Thus, since
,
.
Therefore,
.
Example Question #12 : Fundamental Theorem Of Calculus
Given , what is
?
According to the Fundamental Theorem of Calculus, if is a continuous function on the interval
with
as the function defined for all
on
as
, then
. Therefore, if
, then
. Thus,
.
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