Larson_Calculus_10e ch15sec03
MULTIPLE CHOICE
1. Calculate the line integral along for and C is any path starting at the
point and ending at .
a.
b.
c.
d.
e.
2. Calculate the line integral along for and C is any path starting at the
point and ending at .
a.
b.
c.
d.
e.
3. For the vector field , find the value of A for which the field is conservative.
a.
5
b.
6
c.
4
d.
25
e.
is not conservative for any value of A.
4. Determine whether or not the vector field is conservative.
a.
conservative
b.
not conservative
5. Find the value of the line integral , where and
.
(Hint: If F is conservative, the integration may be easier on an alternate path.)
a.
3,072
b.
192
c.
6,144
d.
6,144
e.
6,912
6. Find the value of the line integral on the closed path consisting of line segments from
to from to and then from to where .
(Hint: If F is conservative, the integration may be easier on an alternate path.)
a.
99
b.
12
c.
36
d.
30
e.
0
7. Find the value of the line integral .
(Hint: If is conservative, the integration may be easier on an alternate path.)
a.
243
b.
192
c.
108
d.
0
e.
12
8. Find the value of the line integral .
(Hint: If is conservative, the integration may be easier on an
alternate path.)
a.
b.
c.
d.
e.
9. Find the value of the line integral where C is an ellipse
from to .
(Hint: If is conservative, the integration may be easier on an alternate
path.)
a.
b.
c.
8
d.
e.
10. Find the value of the line integral , where and
.
(Hint: If F is conservative, the integration may be easier on an alternate path.)
a.
4
b.
8
c.
4
d.
–4
e.
–8
11. Find the value of the line integral where and
.
(Hint: If F is conservative, the integration may be easier on an alternate path.)
a.
–24
b.
48
c.
–48
d.
24
e.
0
12. Evaluate the line integral using the Fundamental Theorem of Line Integrals. Use a computer algebra
system to verify your results.
C: a smooth curve from to
a.
30
b.
15
c.
13
d.
56
e.
169
13. Evaluate the line integral using the Fundamental Theorem of Line
Integrals, where C is the line segment from to .
a.
–2
b.
–1
c.
2
d.
1
e.
0
14. Evaluate the line integral using the Fundamental Theorem of Line Integrals. Use a computer algebra
system to verify your results.
C: circle clockwise from to
a.
b.
c.
d.
e.
15. Evaluate the line integral using the Fundamental Theorem of Line
Integrals, where C is the smooth curve from to .
a.
274
b.
298
c.
300
d.
30
e.
272
16. Find the work done by the force field in moving an object from P to Q.
a.
27,992
b.
55,985
c.
83,978
d.
41,989
e.
69,982
17. A stone weighing 2 pounds is attached to the end of a four-foot string and is whirled horizontally with
one end held fixed. It makes 1 revolution per second. Find the work done by the force F that keeps the
stone moving in a circular path. [Hint: Use Force = (mass)(centripetal acceleration).] Round your
answer to two decimal places, if required.
a.
201.06
b.
0.00
c.
804.25
d.
256.00
e.
12.57