Math 166
Summer 2002
Exam 1
- (45 pt)Evaluate the
following integrals:
a)
b)
c) ![](./M166.1.SU2002_files/image006.gif)
d)
e)
- (15 pt) (Scaling a
function) Find a value of
so that the
function
has average
value equal to 1 on the interval ![](./M166.1.SU2002_files/image016.gif)
- (20 pt) Consider the
functions
and ![](./M166.1.SU2002_files/image020.gif)
a)
Find
the area of the region enclosed by the two curves.
b)
Find
the volume obtained when the part of this region on the right side of the
axis is revolved about the line ![](./M166.1.SU2002_files/image024.gif)
- (10 pt) A cylindrical
tank of height
with a circular base of radius
(both measured
in feet) is filled with a fluid that is
pounds per cubic foot. Find the work done in pumping the
fluid out of the tank.
- (10 pt) Suppose that
you have a solid object and you compute the volume using decreasing
cross-sectional areas from the base to height
You find that you get the formula
How tall is the
object? (Hint: find
so that the
cross-sectional area is 0).
![](./M166.1.SU2002_files/image041.gif)
- (10 pt) Find the volume
obtained when the region in the first quadrant bounded by
and
is revolved about the
axis. What happens to your answer as
What happens to
your answer as
What should
happen?