Math 208 (Lutz) - Quiz #8, 4/4/14
Name:
Directions: This quiz has 2 questions, for a total of 20 points. Solve each problem carefully. You must
show ALL of your work in order to earn full credit.
1. Consider the vector field F! = 2y!i + (2x + 2y)!j.
(a) (5 points) Find a potential function for F! .
!
(b) (5 points) Evaluate C F! · d!r, where C consists of the arc of the circle x2 + y 2 = 4 from (2, 0) to
(0, 2), followed by the line segment to (3, 4).
!
2. (10 points) Use Green’s Theorem to evaluate the line integral C F! · d!r, where F! = xy!j, and C is the
counterclockwise path around the boundary of the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1.