Number 
Question 
Answer 
See the work 
1.

Find the volume of the solid obtained by rotating the region bounded by
about the y axis

15.70796 
The work
Point Cost: 3 
2.

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region
bounded by and about the y axis.

1.885 
The work
Point Cost: 4 
3.

Use the method of cylindrical shells to find the volume
of the solid obtained by rotating the region bounded by
, x= 0 and y= 3, about the x axis.

39.178066 
The work
Point Cost: 3 
4.

The region bounded by y= x and
is rotated about the line x = 5. Using cylindrical shells, set up an integral for the volume of the resulting solid. The limits of integration are: a= b= and the function to be integrated is:

a= 0 b= 1

The work
Point Cost: 1 
5.

The region bounded by and is
rotated about the line x = 1. Using cylindrical shells, set up an integral for the volume of the resulting solid. The limits of integration are: a= b= and the function to be integrated is:

a= 0
b= 1

The work
Point Cost: 1 
6.

The region bounded by , y=0, x=0 and x= 2 is rotated about the line x=2. Using cylindrical shells, set up an integral for the volume of the resulting solid. The limits of integration are: a= b= and the function to be integrated is:

a= 0 b= 2

The work
Point Cost: 1 
7.

Use the method of cylindrical shells to find the
volume generated by rotating the region bounded by
y=0, x=0, and x=1 about the yaxis.

1.98587

The work
Point Cost: 3 
8.

The region bounded by ,
and x=9 is rotated about the line y=10. Using cylindrical shells, set up an integral for the volume of the resulting solid. The limits of integration are: a= b= and the function to be integrated is:

a= 8
b= 8

The work
Point Cost: 2 