Larson_Calculus_10e ch15sec07
MULTIPLE CHOICE
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.
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.
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.
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.
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
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.
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.