Math 208 (Lutz)
Review Exercises: 17.5, 18.1 - 18.4, 19.1 - 19.2
11/21/13
1. Compute the flux of F! = y!i − x!j + z!k through the sphere of radius 1 centered at the origin,
oriented outward.
!
2. Use Green’s Theorem to evaluate C (y 2!i + x!j) · d!r, where C is the counterclockwise path
around the perimeter of the rectangle 0 ≤ x ≤ 2, 0 ≤ y ≤ 3.
3. Find parametric equations for the sphere centered at the point (2, −1, 3) and with radius 5.
!
4. Evaluate the line integral C F! · d!r, where F! = 2xy!i + xy!j, and C is the portion of the
parabola y = 2x2 + 1 from (0, 1) to (1, 3).
5. Compute the flux of F! = x!i + y!j + z!k over the quarter cylinder S given by x2 + y 2 = 1,
0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ z ≤ 1, oriented away from the z-axis.
6. Evaluate the line integral
from (1, 1) to (5, 25).
!
C
(3x2!i + 4y!j) · d!r, where C is the portion of the parabola y = x2
7. Calculate the flux of F! = x2!i + y 2!j + z!k through the cone z =
with x2 + y 2 ≤ 1, x ≥ 0, y ≥ 0.
!
x2 + y 2 , oriented upward,
8. Find a potential function for the vector field F! = F1!i + F2!j, where
F1 =
2 cos2 x
2
− 2 cos x sin x ln(2x + y) + 4e2y cos(4x + y) + 3x2 y,
2x + y
F2 =
cos2 x
2
2
+ 4ye2y sin(4x + y) + e2y cos(4x + y) + x3 .
2x + y