1. ) Find the area of the region between the
two curves 
, 
, 
and 
.
2. ) Find the volume of the solid obtained by
rotating the region ,
, enclosed by the given curves 
, 
, 
, 
about the x-axis.
3. ) Find the
volume of the solid obtained by rotating the region ,
, enclosed by the
curves 
and 
about the line 
.
4. ) Use the method of cylindrical shells to
find the volume of the solid obtained by rotating the region bounded by the
given curves about the x-axis : 
, 
.
5. ) Use the method of cylindrical shells to find the volume of the solid obtained by
rotating the region bounded by the
given curves about the y-axis : 
, 
.
6. ) Find the work required to pump all the water out of a hemisphere that is full of water that has radius of length 8 meters.
7. ) Find c
such that 
for the function 
on the interval 
.
8. ) If
f is continuous and 
. Show that f
takes on the value 4 at least once on the interval 
.