MATH 2415 -Quiz 7 -Smalley
Sections 15.1 -15.4
-Quiz 7 -Smalley
Sections 15.1 -15.4

Evaluate the line integral of f(x,y) along the curve C.

1) f(x, y) =
x2 +
y2, C: y =
4x + 2, 0 = x = 3
A) 79 17 B) 543 17 C) 237 D) 237 17

Evaluate the line integral along the curve C.

2) +
(xz +
y2) ds, C is the curve r(t) =
(-7 -2t)i +
tj -2tk , 0 = t = 1

C
A) 26
3
B) 26 C) 16
3
D) -16

Find the work done by F over the curve in the direction of increasing t.
3) F =
10zi +
3xj +
7yk; C: r(t) = ti + tj + tk, 0 = t = 1

A) W =
10 B) W =
20 C) W =
40 D) W =
20

3

4) F = xyi +
8j +
3xk; C: r(t) = cos 8ti + sin 8tj + tk, 0 = t d
p

16
25 209 193

A) W =
B) W =
C) W = 0 D) W =

3 24 24

Test the vector field F to determine if it is conservative.
5) F = xyi + yj + zk
A) Conservative B) Not conservative

Find the potential function f for the field F.
6) F =
(y – z)i +
(x + 2y – z)j -(x + y)k
A) f(x, y, z) = xy +
y2 -xz -yz + C B) f(x, y, z) = x +
y2 -xz -yz + C
C) f(x, y, z) = x(y +
y2) -xz -yz + C D) f(x, y, z) = xy +
y2 -x -y + C

Evaluate the work done between point 1 and point 2 for the conservative field F.
7) F =
2xi +
2yj +
2zk; P1(2, 2, 5) , P2(3, 6, 9)
A) W =
159 B) W = 0 C) W =
93 D) W =
-93

Find the divergence of the field F.
8) F =
-6x7i -8xyj -4xzk
A) -42×6 -12x B) -54 C) -42×6 -8y -4z D) -42×6 -12x -54

Apply Green’s Theorem to evaluate the integral.

9)

(x +
2y)dx +
4xy dy; C the the triangle with vertices (0, 0), (3, 0) and (0, 3).

C
A) 27 B) 18 C) 9 D) 54

Using Green’s Theorem, compute the counterclockwise circulation of F around the closed curve C.

1

10) F =
–
8(x2 +
y2)4 i; C is the region defined by the polar coordinate inequalities 1 = r d
2 and 0 d
. d
p
127 129 127

A) B) C) 0 D)

448 448 448