Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
15.6 Surface Integrals 947
15.6 Surface Integrals
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Evaluate , where
.
a.
b.
c.
d.
e.
____ 2. Evaluate , where .
a.
b.
c.
d.
e.
____ 3. Evaluate , where S is , first octant.
a.
b.
c.
d.
948 Chapter 15: Vector Analysis
____ 4. Use a computer algebra system to evaluate where S is
. Round your answer to two decimal places.
a. 124.82
b. 1.07
c. 62.41
d. 141.01
e. 64.00
____ 5. Use a computer algebra system to evaluate where S is
. Round your answer to two decimal places.
a. –475.02
b. –496.00
c. –203.00
d. –971.38
e.
____ 6. Find the mass of the surface lamina S of density .
a.
b.
c.
d.
e.
____ 7. Evaluate , where
.
a.
b.
c.
d.
e.
15.6 Surface Integrals 949
____ 8. Evaluate , where and S is given by
.
a. 8
b. 32
c. 16
d. 96
e. 512
____ 9. Evaluate , where and S is given by
.
a. 10,000
b.
c.
d.
e.
____ 10. Evaluate , where and S is given by
.
a.
b.
c.
d.
e.
950 Chapter 15: Vector Analysis
____ 11. Evaluate , where
.
a.
b.
c.
d.
e.
____ 12. Find the flux of through S, , where is the upward unit normal vector
to S.
, first octant
a.
b.
c.
d.
e.
15.6 Surface Integrals 951
____ 13. Find the flux of through S, , where is the upward unit normal vector
to S.
a.
b.
c.
d.
e.
____ 14. Find the flux of through
where N is the upward unit normal vector to S.
a. 8
b. 11
c. 1
d.
e. 4
____ 15. Find the flux of over the closed surface (let be the outward unit normal vector
of the surface).
S: cube bounded by
a. 200
b. 800
c. 400
d. 1,000
e. 600
952 Chapter 15: Vector Analysis
____ 16. Let be an electrostatic field. Use Gauss's Law to find the total
charge enclosed by the closed surface consisting of the hemisphere and its circular
base in the xy-plane.
a.
b.
c.
d.
e.
____ 17. Find for the lamina with uniform density of 1. Use a
computer algebra system to verify your result.
a.
b.
c.
d.
e.
____ 18. Let S be the surface oriented upwards. Use a computer
algebra system to find the rate of mass flow of a fluid of density through S if the velocity field is
given by .
a.
b.
c.
d.
e.
15.6 Surface Integrals 953
15.6 Surface Integrals
Answer Section
MULTIPLE CHOICE
