Math 161

Spring 2000

Exam 1

 

  1. (40 pt) Evaluate the following integrals:

a)          b)               c)

 

d)       e)

 

  1. (12 pt) Find the volume obtained when the upper half of the ellipse  is revolved about the axis.

 

  1. (10 pt) Write down the partial fraction decomposition of the rational function:

      (do not solve for the constants!)

 

  1. (12 pt) Find the average value of the function  on the interval [0,p]. What happens to the average value as ? Explain.

 

  1. (12 pt) An aquarium that has base length 1m, base width 2m, and height 1m is full of water. Assume that water has density 1000 kg/m3 and that g=9.8 m/s2. Find the work done in pumping the tank dry.

 

  1. (24 pt) Consider the following picture:

 


                                               

 

 

 

 

                                                   

 

 

 

 

      Find the volume obtained by revolving the region bounded by , and the axis about the axis. When you get your answer, take the limit as . What did you get, and what should you get?