Answers to Exam Review Questions

Question 1, c The surface integral over the side is 0, over the top is pi*L*a^2, and over the bottom is 0. Thus, the total surface integral is pi*L*a^2. The triple integral of the divergence is also pi*L*a^2, as it should be by the Divergence Theorem.

Question 1, d The surface integral and the line integral are both 0.

Question 1, e The surface integral and the line integral are both 0.

Question 2 This was done in class.

Question 3 26/sqrt(10)

Question 4, c 1/2

Question 5 4 pi/3

Question 6 6x + 16y -z = 34

Question 7 saddle point at x = 12 and y = 8

Question 8 r(t) = 2 cos(t) i + 3 sin(t) j;
integral of sqrt(4 sin^2 (t) + 9 cos^t(t)) from t = 0 to 2 pi.

Question 9 (16 pi/3)*(1-sqrt(3)/2)

Question 10 -pi/2

Question 11 16

Question 12 3 pi/4

Question 13 -1

Question 14 2916 pi/5

Question 15 4*pi

Lawrence C. Moore < lang@math.duke.edu>

Last modified: December 17, 1997