
Understanding Green's Theorem and Line Integrals
Interactive Video
•
Mathematics
•
11th Grade - University
•
Hard
Standards-aligned

Ethan Morris
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the orientation of the region in Green's Theorem examples discussed in the video?
Counterclockwise with the region to the right
Clockwise with the region to the right
Counterclockwise with the region to the left
Clockwise with the region to the left
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In Green's Theorem, what does the line integral along a closed path equal?
The single integral of the partial of p with respect to x minus the partial of q with respect to y
The single integral of the partial of q with respect to x minus the partial of p with respect to y
The double integral of the partial of q with respect to x minus the partial of p with respect to y
The double integral of the partial of p with respect to x minus the partial of q with respect to y
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What are the boundaries of the region defined in the problem?
x from 0 to 2, y from 2x to 2x^2
x from 0 to 1, y from 2x to 2x^2
x from 0 to 1, y from 2x^2 to 2x
x from 0 to 2, y from 2x^2 to 2x
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the expression for f in the given problem?
f(x, y) = x^2 + y^2 i + 2xy j
f(x, y) = x^2 - y^2 i + 2xy j
f(x, y) = x^2 + y^2 i - 2xy j
f(x, y) = x^2 - y^2 i - 2xy j
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of the partial derivative of Q with respect to x?
-2y
2x
2y
0
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the simplified expression inside the integral after applying Green's Theorem?
2y
4y
0
-4y
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the antiderivative of 4y with respect to y?
2y^2
y^2
8y^2
4y^2
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