FALL 2009 MATH 223 MIDTERM EXAM (2)
Answer all questions. Show all work and simplify answers. Calculators
are not permitted. Each problem is worth 5 points
Problem 1. Let the vector field F(x, y) = (x +y) 2i + yj describing a fluid
flow in the xy-plane. Let C be the unit circle x 2 + y2 = 1. Find the net
outward flow.
Problem 2. Calculate the line integral fc, xy4 ds, where C is the left half
of the unit circle x2 + y2 = 1.
Problem 3. Find the work done by the vector field F(x, y, z) = (x y)i +
y2j + (x — z)k on a particle that moves along the line segment from
(1,2,1) to (0,3,-5).
Problem 4. Let F(x, y) = (4x3 + 9x2y2, 6x3y + 6y5). Calculate the line
integral fc F • dr, where C is the line segment from (0,1) to (1,2).
Problem 5. Let F(x, y) = <y, —x>. Calculate the line integral fc F • dr,
where C is the positively oriented triangle with vertices (0, —1), (1,0)
and (0, 1).
Date: November 13, 2009 Jitsukawa.
NOTE: fc = line integral along C