_______________________________________________________________________
Calculus  II                                                 Test #2                                      March 19, 2004

Name____________________           R.  Hammack                                     Score ______
______________________________________________________________________

(1) Find the area of the region contained between the graphs of y = e^x,  y = e^(2x), and x = ln(3).
Simplify your final answer as much as possible.




(2) Consider the region contained between the curves y = x^2 and  y = x^(1/2).
This region is revolved around the x-axis. What is the volume of the resulting solid?





(3) Consider the region contained between the graph of y = 1/x,  y = 0, x = 1, and x = 3.
This region is revolved around the y-axis. Find the volume of the resulting solid.

 




(4) Find the arc length of the curve y = x^(1/3)^2  over the interval 1≤x≤8.

 




(5) Consider the graph of y = x^3 for 0≤x≤1. This curve is revolved around the x-axis.
Compute the area of the resulting surface.

 




(6) A cylindrical tank, filled with water,  is 10 meters high, and has a radius of 10 meters. Calculate the work required to pump all the water to the top of the tank. Assume that just enough work is done to overcome the force of gravity. (Recall that the density of water is 1000 kilograms per cubic meter, and the acceleration due to gravity is 9.8 meters per second per second.)