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954 Chapter 15: Vector Analysis
15.7 Divergence Theorem
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Use the Divergence Theorem to evaluate Verify your answer by
evaluating the integral as a triple integral.
S: cube bounded by the planes
a.
b.
c.
d.
e.
____ 2. Let and let S be the cylinder
Verify the Divergence Theorem by evaluating as a surface integral and as a triple integral.
a.
b.
c.
d.
e.
15.7 Divergence Theorem 955
____ 3. Let and let S be the surface bounded by the
plane and the coordinates planes. Verify the Divergence Theorem by evaluating
as a surface integral and as a triple integral.
a.
b.
c.
d.
e.
956 Chapter 15: Vector Analysis
____ 4. Let and let S be the surface bounded by the planes
and the coordinate planes. Verify the Divergence Theorem by evaluating
as a surface integral and as a triple integral. Round your answer to two decimal places
wherever applicable.
a.
b.
c.
d.
e.
____ 5. Let and let S be the surface bounded by
and . Verify the Divergence Theorem by evaluating as a surface integral
and as a triple integral. Round your answer to two decimal places.
a.
b.
c.
d.
e.
15.7 Divergence Theorem 957
____ 6. Let and let S be the surface bounded by
and . Verify the Divergence Theorem by evaluating as a surface
integral and as a triple integral. Round your answer to two decimal places.
a.
b.
c.
d.
e.
____ 7. Use Divergence Theorem to evaluate and find the outward flux of
through the surface S of the solid bounded by the planes
.
a.
b.
c.
d.
e.
____ 8. Use the Divergence Theorem to evaluate and find the outward flux of
through the surface of the solid bounded by the graphs of the equations. Use a computer algebra
system to verify your results.
a.
b.
c.
d.
e.
958 Chapter 15: Vector Analysis
____ 9. Use Divergence Theorem to evaluate and find the outward flux of
through the surface S of the solid bounded by the sphere .
a.
b.
c.
d.
e.
____ 10. Use the Divergence Theorem to evaluate and find the outward flux of
through the surface of the solid bounded by the graphs of the equations. Use a computer algebra
system to verify your results.
a.
b.
c.
d.
e.
____ 11. Use Divergence Theorem to evaluate and find the outward flux of
through the surface S of the solid bounded by
a.
b.
c.
d.
e. 0
15.7 Divergence Theorem 959
____ 12. Use Divergence Theorem to evaluate and find the outward flux of
through the surface S of the solid bounded by the planes
.
a.
b.
c.
d.
e.
____ 13. Use the Divergence Theorem to evaluate and find the outward flux of
through the surface of the solid bounded by the graphs of the equations. Use a computer algebra
system to verify your results.
a.
b.
c.
d.
e.
960 Chapter 15: Vector Analysis
____ 14. Evaluate , where and
S is the closed surface of the solid bounded by the graphs , , and the coordinate
planes.
a.
b.
c.
d.
e.
____ 15. Evaluate where S is the closed surface of the solid bounded by the
graphs of
a.
b.
c.
d.
e.
____ 16. Let and let S be the cube bounded by the planes
. Verify the Divergence Theorem by evaluating as a surface
integral and as a triple integral.
a.
b.
c.
d.
e.
15.7 Divergence Theorem 961
15.7 Divergence Theorem – Answer Section
