_______________________________________________________________________________

Calculus II Test
#2 March
21, 2003

Name____________________ R. Hammack Score
______

_______________________________________________________________________________

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

(2) Consider the region contained between
the y axis and the curve .
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 ,
,
,
and .

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

(4) Find the exact arc length of the curve
from x = 0 to x
= 3.

(5) Consider the graph of
for .
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.)