Understanding Green's Theorem and Line Integrals

Understanding Green's Theorem and Line Integrals

Assessment

Interactive Video

Mathematics

11th Grade - University

Hard

CCSS
7.NS.A.1C

Standards-aligned

Created by

Ethan Morris

FREE Resource

Standards-aligned

CCSS.7.NS.A.1C
The video tutorial explains how to use Green's theorem to solve line integrals. It begins with a clarification of the theorem, emphasizing the importance of the region's orientation. The instructor sets up a problem involving a specific curve and boundary conditions, then applies Green's theorem to solve the integral. The process involves calculating partial derivatives and antiderivatives, ultimately finding the solution to the integral. The tutorial concludes with a brief mention of a future example.

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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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