Math 166
Fall 2001
Final Exam
a) b) c) d)
a)
Find
the area between the two curves.
b)
Find
the volume obtained when the region bounded by the curves is revolved about the
axis.
c)
Find
the length of the curve (hint: 1 d) might be
useful).
d)
Find
the surface area obtained when is revolved about the
axis.
a) b) where each is between 0 and 9.
a) b) c)
a)
Sketch
both curves (indicating which is which).
b)
Find
the area that is common to both curves (that is, the area inside both
curves).
USEFUL STUFF: