Math 166

Fall 2001

Exam 1

 

  1. (48 pt) Evaluate the following integrals:

 

a)         b)         c)         d)

 

e)                        f)

 

  1. (10 pt) Find the area between the curves  () and

 

  1. (10 pt) Find the volume obtained when the region between the curves  and is revolved about the line
  2. (12 pt) Find the volume obtained when the right half of the ellipse  is revolved about the axis. What happens to your answer if you let  What should happen?

 

  1. (15 pt) Find the volume obtained when the region bounded by the lines  (), the line  and the axis is revolved about the  axis. What happens to your answer as  What should happen?

 

 


                                                                    y=h-(h/R)x

                                        

 


                                                     y=h-mx

 

 

  1. (15 pt)You pull up an object attached to an 80-foot rope to the top of a 320-foot building. If the rope weighs 0.5 pounds per foot and the amount of work done in hoisting the object to the top of the building is 9600 foot pounds, then how much does the object weigh?