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Calculus II Test
#2 March
19, 2004

Name____________________ R. Hammack Score
______

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(1) Find the area of the region contained
between the graphs of , ,
and .

Simplify your final answer as much as possible.

(2) Consider the region contained between
the curves
and .

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 , ,
,
and .

This region is revolved around the y-axis.
Find the volume of the resulting solid.

(4) Find the arc length of the curve
over
the interval .

(5) Consider the graph of
for .
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.)