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Discussion week 12Questions1. Why do we use Green’s Theorem to solve integrals?2. Complete the proof of the special case of Green’s Theorem by proving equations 3test book) See the file belowPeer Responses Respond to at least two of your peers, and comment on their application.Do you agree with their reasoning for the use of Green’s theorem and the proof or just something you find interesting Please remember proper netiquette…make sure your responses to your peers are polite. Thank you!

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due Apr 27

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Discussion week 12

Initial Post

Make your initial post by Tuesday 11:59 pm

1. Why do we use Green’s Theorem to solve integrals?

2. Complete the proof of the special case of Green’s Theorem by proving equations 3 ∫𝐶

𝑄𝑑𝑦 = ∫ ∫

∂𝑄

𝐷

∂𝑥

𝑑𝐴

(see page 1103 of the

test book)

Peer Responses

Respond to at least two peers by Thurday 11:59 pm

Respond to at least two of your peers, and comment on their application.

Do you agree with their reasoning for the use of Green’s theorem and the proof or just something you find interesting

Please remember proper netiquette…make sure your responses to your peers are polite. Thank you!

Resources

Canvas guides and supplemental resources are provided to help you complete each activity.

How do I reply to a discussion? (https://community.canvaslms.com/docs/DOC-10561-4212190706)

Grading Rubric

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Reply

(https://

Thao Chung (https://sdccd.instructure.com/courses/2417891/users/8705133)

Saturday

1. We use Green’s Theorem because we can compute two different types of integrals when they are equal to each other.

Green’s theorem can transform a line integral into a double integral, and it can be used to transform a double integral into a line

integral that helps us to find the area of function easier.

2. I attached the paper with proof of the special case of Green’s Theorem below.

Proof of special case of Green’s Theorem.pdf (https://sdccd.instructure.com/files/136503993/download?

download_frd=1&verifier=s7cfVMxba0D24JAgJq2XiF3ykSbGc3ItAeY6GO9s)

Reply

(https://

Angie Padua (https://sdccd.instructure.com/courses/2417891/users/8701792)

Yesterday

Green’s theorem gives a relationship between the line integral over a closed path on a plane and the double integral over the

region that is enclosed. The region is both vertically and horizontally. It can be used only for vector fields in two dimensions and it

cannot be used in vector fields that are in three dimensions. The theorem is only valid for curves that are oriented

counterclockwise.

Reply

Daniel：

1.We use Green’s theorem in order to compute the line integrals of a curve that encloses a region.

The theorem can transform the line integral of the curve to a double integral over the region

enclosed by the curve, which creates a relationship between the two types of integrals. This can

make it easier to find the area of a region.

2.(The special case of the theorem is attached below.)

Christian：

1) Green’s Theorem is used because it shows the relationship between a line integral over a

closed path and the double integral at the region that is enclosed.

2)(The special case of the theorem is attached below.)

Initial Post

Make your initial post by Tuesday 11:59 pm

1. Why do we use Green’s Theorem to solve integrals?

2. Complete the proof of the special case of Green’s Theorem by proving equations 3 Sc Qdy = | lood A (see page 1103 of the

test book)

Peer Responses

Respond to at least two peers by Thurday 11:59 pm

Respond to at least two of your peers, and comment on their application.

Do you agree with their reasoning for the use of Green’s theorem and the proof or just something you find interesting

Please remember proper netiquette…make sure your responses to your peers are polite. Thank you!

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Tags:

line integrals

Green theorem

Theorem Purpose

curve circulation

closed paths

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