CUCNY Wk 12 The Purpose of The Green Theorem and Line Integrals Discussion

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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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This is a graded discussion: 20 points possible
due Apr 27
Since this is a group discussion, each group has its own conversation for this topic. Here are the ones you have access to:
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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
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Thao Chung (https://sdccd.instructure.com/courses/2417891/users/8705133)
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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)
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(https://
Angie Padua (https://sdccd.instructure.com/courses/2417891/users/8701792)
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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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