Math 166
Fall 2001
Exam 2
- (24 pt) Evaluate the
following integrals (or show that they do not converge).
a)
b)
c)![](./M166.2.F2001_files/image006.gif)
- (10 pt) Let
Show that
converges.
- (15 pt) Use the arc length integral to show that the circumference
of a circle of radius
is given by ![](./M166.2.F2001_files/image014.gif)
- (15 pt) Find the surface area obtained when the parabola
is revolved about the
axis. What happens to your answer as
What should
happen?
- (24 pt) Consider the function
For this problem, you can use the fact that ![](./M166.2.F2001_files/image024.gif)
a)
Find
the volume obtained when the region bounded by
and the
axis is revolved about the
axis.
b)
Find
the volume obtained when the region bounded by
and the
axis is revolved about the
axis.
c)
Use
your results from a) and b) to locate the centroid of the region bounded by
and the
axis.
- (10 pt) Suppose you want to use Simpson’s rule to estimate
Find the minimal
so that using
gives an error
bound less than or equal to .05. The fourth derivative of
is pictured
below.
- (12 pt) Water is contained in a glass aquarium in the shape of a
cube. Each side of the aquarium is 2 feet long. Find the force due to
hydrostatic pressure exerted on each side of the aquarium. (Remember that
force is pressure times area and that in our system of units, pressure is
depth times 62.5).