# Is my proof of greens theorem correct?

• okkvlt
In summary, Green's Theorem is a fundamental theorem in multivariable calculus that relates a line integral around a simple closed curve to a double integral over the region enclosed by the curve. It is named after the mathematician George Green. To ensure the correctness of a proof of Green's Theorem, one can compare it to a known proof, carefully check for mistakes, or seek feedback from others. Common mistakes when proving Green's Theorem include incorrect application or use of variables, and computational errors. It can only be used in simply connected regions without any holes or gaps. Green's Theorem is important in mathematics and science because it simplifies difficult integrals, has applications in physics and engineering, and serves as a basis for other important
okkvlt
here it is.
http://img193.imageshack.us/img193/79/greenproof.jpg

#### Attachments

• greenproof.jpg
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i know that's why u got to click on the link to the pic, don't go through the attachment.

Even after cllicking on it, opening in a new window, and then "enlarging", it is still too small to be read comfortably.

In the browser I'm using, Firefox, clicking on the picture makes it bigger and readable. Of course, I haven't used Green's Theorem in years so I'm completely useless

im using firefox too. must be the browser then

## What is Green's Theorem?

Green's Theorem is a fundamental theorem in multivariable calculus that relates a line integral around a simple closed curve to a double integral over the region enclosed by the curve. It is named after the mathematician George Green.

## How do I know if my proof of Green's Theorem is correct?

There are a few ways to check if your proof of Green's Theorem is correct. One way is to compare your proof to a known and verified proof of the theorem. Another way is to carefully check each step of your proof for any mistakes or errors. You can also ask a colleague or a professor to review your proof and provide feedback.

## What are the common mistakes when proving Green's Theorem?

Some common mistakes when proving Green's Theorem include incorrect application of the theorem, incorrect use of variables, and computational errors. It is also important to make sure that all assumptions and conditions of the theorem are satisfied in your proof.

## Can Green's Theorem be used in any region?

No, Green's Theorem can only be used in regions that are simply connected, meaning they do not contain any holes or gaps. If the region is not simply connected, then Green's Theorem cannot be applied.

## Why is Green's Theorem important in mathematics and science?

Green's Theorem is important because it allows us to convert a difficult line integral into a simpler double integral, making it easier to solve. It also has many applications in physics and engineering, especially in the fields of electromagnetism and fluid dynamics. Additionally, Green's Theorem is a fundamental theorem that serves as a basis for other important theorems in calculus, such as Stokes' Theorem and the Divergence Theorem.

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