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  .