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15.2 Line Integrals 911
15.2 Line Integrals
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find a piecewise smooth parametrization of the path C given in the following graph.
a.
b.
c.
d.
912 Chapter 15: Vector Analysis
e.
____ 2. Find a piecewise smooth parametrization of the path C given in the following graph.
a.
b.
c.
d.
e.
____ 3. Evaluate the line integral along the given path.
a.
b.
c.
d.
e.
15.2 Line Integrals 913
____ 4. Evaluate along the path C, defined as counterclockwise along the
circle from to .
a.
b.
c.
d.
e.
____ 5. Evaluate along the path C, defined as y-axis from .
a.
b.
c.
d.
e.
____ 6. Find the total mass of the wire with density .
a.
b.
c.
914 Chapter 15: Vector Analysis
d.
e.
____ 7. Evaluate where C is represented by .
a.
b.
c.
d.
e.
____ 8. Evaluate where C is represented by .
a.
b.
c.
d.
e.
15.2 Line Integrals 915
____ 9. Find the work done by the force field on a particle moving along the given path.
from to .
a.
b.
c.
d.
e.
____ 10. Evaluate where and
.
a.
b.
c.
d.
e.
____ 11. Evaluate the integral along the path C, defined as y-axis
from .
a.
b.
c.
d.
e.
916 Chapter 15: Vector Analysis
____ 12. Evaluate the integral along the path C, defined as
from
a.
b.
c.
d.
e.
____ 13. Find the area of the lateral surface over the curve C in the xy-plane and under the
surface where Lateral surface .
line from .
a.
b.
c.
d.
e.
____ 14. A tractor engine has a steel component with a circular base modeled by the vector-
valued function . Its height is given by . (All measurements of the
component are given in centimeters.) Find the lateral surface area of the component. Round your
answer to two decimal places.
a.
b.
c.
d.
e.
15.2 Line Integrals 917
____ 15. Find the moments of inertia for a wire that lies along
with density .
a.
b.
c.
d.
e.
____ 16. Find the work done by a person weighing pounds walking exactly one revolution
up a circular helical staircase of radius feet if the person rises feet.
a.
b.
c.
d.
e.
918 Chapter 15: Vector Analysis
15.2 Line Integrals
Answer Section
MULTIPLE CHOICE
