I need help with these 20 questions, thanks, show some work, doesnt need to be too detialedE
1.
(1 pt)
Using disks or washers, fnd the volume oF the solid obtained
by rotating the region bounded by the curves
y
=
1
/
x
,
y
=
0
,
x
=
1
,
and
x
=
2 about the
x

axis.
Volume =
2.
(1 pt)
Using disks or washers, fnd the volume oF the solid obtained
by rotating the region bounded by the curves
y
=
p
x

1
,
y
=
0
,
x
=
2
,
and
x
=
5 about the
x
axis.
Volume =
3.
(1 pt)
Using disks or washers, fnd the volume oF the solid obtained
by rotating the region bounded by the curves
y
=
sec
(
x
)
,
y
=
1
,
x
=

1
,
and
x
=
1 about the xaxis.
Volume =
4.
(1 pt)
Using disks or washers, fnd the volume oF the solid obtained
by rotating the region bounded by the curves
y
=
x
2
and
y
=
4
about the line
y
=
4
.
Volume =
5.
(1 pt)
Which oF the Following integrals represents the volume oF
the solid obtained by rotating the region bounded by the curves
y
=
sin
(
x
)
and
y
=
0
,
with 0
?
x
?
p
about the line
y
=
1?
•
A.
p
Z
1
0
[
1
2

(
1

sin
(
x
))
2
]
dx
•
B.
p
Z
1
0
[
1

sin
2
(
x
)]
dx
•
C.
p
Z
p
0
[(
1
)

(
1

sin
(
x
))]
2
dx
•
D.
p
Z
1
0
[(
1
)

(
1

sin
(
x
))]
2
dx
•
E.
p
Z
p
0
[
1

sin
2
(
x
)]
dx
•
±.
p
Z
p
0
[
1
2

(
1

sin
(
x
))
2
]
dx
6.
(1 pt)
Using disks or washers, fnd the volume oF the solid obtained
by rotating the region bounded by the curves
y
=
x
,
y
=
0
,
x
=
2
,
and
x
=
4 about the line
x
=
1
.
Volume =
7.
(1 pt)
Call an improper defnite integral type 1 iF it is improper be
cause the interval oF integration is infnite.
Call it type 2 iF it is improper because the Function takes on
an infnite value within the interval oF integration.
ClassiFy the type(s) For each oF the Following improper inte
grals.
?
1.
Z
0

•
1
x
2
+
5
dx
?
2.
Z
2
0
x
x
2

5
x
+
6
dx
?
3.
Z
•
1
x
4
e

x
4
dx
?
4.
Z
p
/
2
0
sec
(
x
)
dx
8.
(1 pt)
Consider the integral
Z
•

•

4
x
1
+
x
2
dx
IF the integral is divergent, type an uppercase ”D”. Otherwise,
evaluate the integral.
9.
(1 pt)
Consider the integral
Z
9
1
8
3
p
x

9
dx
IF the integral is divergent, type an uppercase ”D”. Otherwise,
evaluate the integral.
10.
(1 pt)
Consider the integral
Z
4
0

4
p
x
dx
IF the integral is divergent, type an uppercase ”D”. Otherwise,
evaluate the integral.
Generated by the WeBWorK system c
±
WeBWorK Team, Department oF Mathematics, University oF Rochester
1
Answer