Math 166

Summer 2002

Exam 1

 

  1. (45 pt)Evaluate the following integrals:

a)               b)           c)

 

d)          e)          

 

  1. (15 pt) (Scaling a function) Find a value of  so that the function  has average value equal to 1 on the interval

 

  1. (20 pt) Consider the functions  and

a)      Find the area of the region enclosed by the two curves.

b)      Find the volume obtained when the part of this region on the right side of the axis is revolved about the line

 

  1. (10 pt) A cylindrical tank of height with a circular base of radius  (both measured in feet) is filled with a fluid that is pounds per cubic foot. Find the work done in pumping the fluid out of the tank.

 

  1. (10 pt) Suppose that you have a solid object and you compute the volume using decreasing cross-sectional areas from the base to height You find that you get the formula  How tall is the object? (Hint: find  so that the cross-sectional area is 0).

 

 

 

 

 

 

 


                       

 

 

 

  1. (10 pt) Find the volume obtained when the region in the first quadrant bounded by  and is revolved about the axis. What happens to your answer as  What happens to your answer as  What should happen?