Math 166
Fall 2000
Exam 1
- (40 pt) Evaluate the
following integrals:
a) 
b) 
c) 
d) 
e) 
- (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
a)
Find
the volume obtained when this region is revolved about the line 
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.
