962 Chapter 15: Vector Analysis
15.8 Stokes’s Theorem
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the curl of the vector field .
a.
b.
c.
d.
e.
____ 2. Find the curl of the vector field
a.
b.
c.
d.
e.
____ 3. Find the curl of the vector field
a.
b.
15.8 Stokes’s Theorem 963
c.
d.
e.
____ 4. Verify Stokes’s Theorem by evaluating
as a line integral and as a double integral .
a.
b.
c.
964 Chapter 15: Vector Analysis
d.
e.
____ 5. Let and let S be the plane in the first
octant. Verify Stokes’s Theorem by evaluating as a line integral and as a double
integral.
a.
b.
c.
d. 0
e. 1
____ 6. Let and let S be the graph of
.
Verify Stokes’s Theorem by evaluating as a line integral and as a double
integral.
a.
b.
c.
d.
e.
15.8 Stokes’s Theorem 965
____ 7. Use Stokes’s Theorem to evaluate Use a computer algebra system to verify
your results. Note: C is oriented counterclockwise as viewed from above.
C: triangle with vertices
a.
b.
c.
d.
e.
____ 8. 143. Let and let C be the triangle with
vertices of oriented counterclockwise. Use Stokes’s Theorem
to evaluate
a.
b.
c.
d.
e.
____ 9. Let and let S be the graph of
oriented counterclockwise. Use Stokes’s Theorem to evaluate .
a.
b.
c.
d.
e.
966 Chapter 15: Vector Analysis
____ 10. Use Stokes’s Theorem to evaluate .Use a computer algebra system to
verify your results. Note: C is oriented counterclockwise as viewed from above.
a.
b.
c.
d.
e.
____ 11. Use Stokes’s Theorem to evaluate where and
S is .Use a computer algebra system to verify your result.
a.
b.
c.
d.
e.
____ 12. Use Stokes’s Theorem to evaluate where
and S is over in the first
octant. Use a computer algebra system to verify your result.
a. 0
b.
c.
d.
e.
15.8 Stokes’s Theorem 967
____ 13. Use Stokes’s Theorem to evaluate where
and S is the first-octant portion of
over Use a computer algebra system to verify your result.
a.
b.
c.
d.
e.
____ 14. Use Stokes’s Theorem to evaluate Use a computer algebra system to
verify your results. Note: C is oriented counterclockwise as viewed from above.
a.
b.
c.
d.
e.
968 Chapter 15: Vector Analysis
____ 15. Use Stokes’s Theorem to evaluate where
and S is the first-octant portion of over .
Use a computer algebra system to verify your result.
a.
b.
c.
d.
e.
____ 16. The motion of a liquid in a cylindrical container of radius 1 is described by the
velocity field Find where S is the upper surface of the
cylindrical container.
a.
b.
c.
d. 0
e.
____ 17. The motion of a liquid in a cylindrical container of radius 1 is described by the
velocity field Find where S is the upper surface of the
cylindrical container.
a.
b.
c.
d.
e.
15.8 Stokes’s Theorem 969
15.8 Stokes’s Theorem
Answer Section
MULTIPLE CHOICE