In order to apply Green’s theorem, the line integral of the boundary should be evaluated such...

In order to apply Green’s theorem, the line integral of the boundary should be evaluated such that the integration region inside the boundary lies always on the left as one advances in the direction of integration. What happens if the region lies on the right? How can you apply the theorem then? Explain.

Expert Solution

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Dear student,

yes you are correct ..!! We have have the consider the integration region on left.

If you consider right you will end up getting an negative sign to your actual anwer.

For clarification ,

NOTE THAT THE REGION LIYING ON RIGHT AND LEFT HAS NO MEANING AT ALL.

in one situation if you get your domain on left while walking across the boundary,then to get domain on right you just reverse your direction.This simply means both cases are possible in any problem.but in order to use greens therom one must consider your direction of motion (which is nothing but orientation of the boundary) such that you get domain on left side.

Only we were said that,you walk around the surface such that the domain is on the left side.Then the direction up your head is normal direction.

If you are given with a case were right side domain is considerd then put -ve sign in greens therom and remaining all are same.

Colby Messinger answered 1 year ago

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