The function is
.
Fundamental theorem of calculus :
\If
is continuous on
, then the function
is defined by
is continuous on
and differentiable on
, then
.
Here
.
.
.
Find the critical points by equating
.


.
Critcal points are
and
.
The test intervals are
,
and
.
| \
Interval \ | \
Test Value | \Sign of ![]() | \
Conclusion | \
![]() | \
| \
![]() | \
Decreasing | \
![]() | \
![]() | \
![]() | \
\
Increasing \ | \
![]() | \
![]() | \
![]() | \
Decreasing | \
The function is increasing on the interval
.
The function is increasing on the interval
.