leonard (kml3374) – Homework 04 – staron – (53595)
1
This
printout
should
have
16
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
001
10.0points
Determine if
(i) Express the improper integral
Consequently,
I
is
not convergent
.
002(part1of3)10.0points
leonard (kml3374) – Homework 04 – staron – (53595)
2
3.
I
t
=
−
20
e

3
2
+ 4(
t
+ 2)
e

t/
2
4.
I
t
= 4(3
−
t
)
{
e

3
2
−
e

t/
2
}
5.
I
t
= 20
e

3
2
+ 4(
t
+ 2)
e

t/
2
005
10.0points
Find the total area under the graph of
y
=
7
x
4
(iii) Determine if
lim
t
leonard (kml3374) – Homework 04 – staron – (53595)
3
1.
I
=
3
2
2.
I
is not convergent
correct
3.
I
=
1
3
4.
I
=
2
3
5.
I
= 3
Explanation:
The integral is improper because the in
terval of integration is infinite.
To test for
convergence, therefore, we have to check if
the limit
lim
t
→ ∞
integraldisplay
0
t
3
2
x
−
1
dx
exists. But
integraldisplay
0
t
3
2