Math 230 Calculus IISummer 2004
7 problems, 10 points each
1. Show enough work to justify your answers
2. Don't use calculators for integration.
3. Don't leave until you are sure you've solved all the problems.
(a) Use the graph of
below to estimate
(b) Compare them to
Find the area of the surface of revolution around the
Find the centroid of the region bounded by the curves .
Describe the motion of a particle with position
Suppose the parametric curve is given by Set up, but do not evaluate, the integrals that represent (a) the arc-length of the curve (b) the area of the surface obtained by rotating the curve about the -axis.
Plot the curve
For 5 extra points find the line(s) through the origin tangent to the