Math 208 (Lutz) - Quiz #11, 11/15/13
Name:
Directions: This quiz has 4 questions, for a total of 22 points. Solve each problem carefully. You must
show ALL of your work in order to earn full credit.
!
1. (7 points) Use the Fundamental Theorem of Calculus for Line Integrals to evaluate C F! · d!r, where
F! = y sin(xy)!i + x sin(xy)!j, and C is the portion of parabola y = 2x2 from (1, 2) to (3, 18).
2. (4 points) Decide whether the vector field F! = (x2 + y 2 )!i + 2xy!j is the gradient of a function f . If so,
find f . If not, explain why not.
3. (6 points) Use Green’s Theorem to calculate the circulation of F! = xy!j around the square 0 ≤ x ≤ 1,
0 ≤ y ≤ 1.
4. (5 points) Give a parametrization of the plane that contains the three points (1, 2, 3), (2, 5, 8), (5, 2, 0).
(Hint: First find two non-parallel vectors in the plane.)