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Calculus  II                                                         Test #2                                              March 21, 2003

Name____________________                   R.  Hammack                                             Score ______
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(1) Find the area of the region contained between the graphs of y = 1/x,  y = 1 - 1/x, and x = e.

 




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

 

 


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

 




(4)  Find the exact arc length of the curve y = 2/3x^(1/2)^3 from x = 0 to x = 3.

 


(5) Consider the graph of y = 2x^(1/2) for 0≤x≤8. This curve is revolved around the x-axis. Compute the surface area of the resulting region.

 



(6) A basement is 10 meters long, 10 meters wide, and 5 meters deep. After a heavy rain, the basement floods to a depth of 1 meter. Calculate the work required to pump all the water out to ground level. (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.)