Math 166
Fall 2000
Exam 2
- (24
pt) Evaluate the following integrals:
a) (). b) c)
- (20
pt) a) Find
b) Use the fact that the integral
in a) converges to show that converges for
- (16
pt) Consider the region bounded by ().
a)
Find the centroid of this region.
b)
What happen to the centroid as Does this make sense?
- (12
pt) Suppose that you wish to approximate by Simpson’s rule. What is the smallest value of that you should choose to be sure that your
approximation has error less than or equal to
- (10
pt) Find the surface area generated by revolving the function about the x-axis.
- (10
pt) Find the length of the curve
- (18
pt) a) Find the volume obtained by spinning the rectangle pictured about
the x-axis. (The volume should be in terms of the angle q;
the sides of the rectangle are a and b, and you may assume that the
centroid of the rectangle is “dead center”).
b) What happens
to your answer when q=0
and when q=?
c) For what
value of q
is the volume maximized?