
Understanding the Divergence Theorem and Surface Integrals

Interactive Video
•
Mathematics, Science
•
11th Grade - University
•
Hard

Emma Peterson
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the range of x in the described region?
-1 to 1
-2 to 2
0 to 1
0 to 2
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the divergence theorem help simplify in this context?
The evaluation of a surface integral
The calculation of surface area
The determination of vector field direction
The computation of volume
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the divergence of the given vector field?
x^2 + y^2
2x
x + y + z
0
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In what order is the integration performed?
y, z, x
x, z, y
z, y, x
x, y, z
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the upper bound for y in the integration setup?
1 - x^2
1
2 - z
0
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of integrating 2x with respect to y?
2x
0
2xy
2x(2 - z)
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the expression obtained after integrating with respect to z?
2x(1 - z^2)
2x(2 - 2x^2 - 1/2(1 - 2x^2 + x^4))
2x(1 - x^2)
2x(2 - z)
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