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Example Questions
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,
.
Example Question #161 : Introduction To Integrals
Evaluate the definite integral using the Fundamental Theorem of Calculus.
The antiderivative of
is
.
Evaluating (by the fundamental theorem of calculus) gives us...
Example Question #161 : Introduction To Integrals
Solve
The antiderivative of is
.
Evaluating (by the fundamental theorem of calculus) gives us...
Example Question #161 : Integrals
Evaluate the definite integral using the Fundamental Theorem of Calculus.
The antiderivative of is
.
By evaluating (by the fundamental theorem of calculus) we get...
Example Question #162 : Introduction To Integrals
Evaluate the definite integral using the Fundamental Theorem of Calculus.
The antiderivative of is
.
By evaluating (by the fundamental theorem of calculus) we get...
Example Question #11 : 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,
.
Example Question #13 : 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,
.
Example Question #164 : Introduction To Integrals
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
,
.
Thus,
.
Example Question #165 : Introduction To Integrals
Write in integral form, if
is position and
where
is velocity at time
.
To write position in integral form, we can take advantage of the fundamental theorem of calculus. Since the bounds are and
, and
,
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