Math 166
Fall 2000
Exam 1
- (40 pt) Evaluate the
following integrals:
a)
b)
c) ![](./M166.1.F2000_files/image006.gif)
d)
e) ![](./M166.1.F2000_files/image010.gif)
- (15 pt) (A triangular torus) Find the volume obtained when
the region bounded by the lines
,
, and
is revolved
about the
axis.
- (12 pt) A spring is stretched from a units beyond its natural
length to b units beyond its natural length (
). Show that the work done in this stretch is the
average value of the force (during this stretch) times the length
stretched.
- (16 pt) For this problem consider the right half of the circle
![](./M166.1.F2000_files/image022.gif)
a)
Find
the volume obtained when this region is revolved about the line ![](./M166.1.F2000_files/image024.gif)
b)
What
happens to your answer as
What should happen?
- (15 pt) Find the volume obtained when the region bounded by
is revolved
about the
axis.
- (12 pt) For this problem consider the parabola
Find the value of
such that the
line
divides the
region bounded by the parabola and the
axis into two pieces of equal area.