How to use Green's theorem and area of region formula here?

[Win_odd Dhamnekar]

For a region R bounded by a simple closed curve C, show that the area A of R is [math]A = -\displaystyle\oint_C ydx = \displaystyle\oint_C xdy = \frac12 \displaystyle\oint_C xdy -ydx,[/math]where C is traversed so that R is always on the left. (Hint: Use Green’s Theorem and the fact that A =[imath]\displaystyle\iint\limits_R 1dA)[/imath]

How to answer this question? What is the answer to this question?

Any math help or even correct answer will be accepted.

 

[Dr.Peterson]

For a region R bounded by a simple closed curve C, show that the area A of R is [math]A = -\displaystyle\oint_C ydx = \displaystyle\oint_C xdy = \frac12 \displaystyle\oint_C xdy -ydx,[/math]where C is traversed so that R is always on the left. (Hint: Use Green’s Theorem and the fact that A =[imath]\displaystyle\iint\limits_R 1dA)[/imath]

How to answer this question? What is the answer to this question?

Any math help or even correct answer will be accepted.

What have you tried?

The least you can do is to state Green's Theorem as you were taught it, and suggest some functions you might apply it to. (That is, use the hint!)

I'd also suggest that you try one piece at a time. Try starting with one of the smaller integrals, rather than the largest.

Please don't expect others to do all the work for you. This site is about learning to solve problems yourself, not about getting free answers. (You should know that by now.)

 

[Win_odd Dhamnekar]

What have you tried?

The least you can do is to state Green's Theorem as you were taught it, and suggest some functions you might apply it to. (That is, use the hint!)

I'd also suggest that you try one piece at a time. Try starting with one of the smaller integrals, rather than the largest.

Please don't expect others to do all the work for you. This site is about learning to solve problems yourself, not about getting free answers. (You should know that by now.)

Hi,

Anyone can find answer to this question here.

 

[blamocur]

Hi,

Anyone can find answer to this question here.

I don't think @Dr.Peterson was looking for your help with Green's Theorem. But an explicit statement, instead of a reference to a video, could let us help you with additional hints.

 

[topsquark]

Hi,

Anyone can find answer to this question here.

It's a video. What question are you asking help on? And if it's a new problem it needs to go in a new thread.

-Dan

 

[Deleted member 4993]

What have you tried?

I do not think the video answers this question - most important question to be answered in our opinion.