Integral with c as an ellipse

[bugatti79]

Folks,

Use green's theorem to evalute the following with c = x^2+xy+y^2

\(\displaystyle \int_c sin(y) dx + x cos(y) dy\)

I calculate

\(\displaystyle \int \int_R (cos y -cos y ) dA = 0\)........?

I thought that if the curve is simple and closed but includes the origin then we expect some non 0 value?

Thanks

 

[tkhunny]

1) It's not perfectly clear to me what your curve is. Is "c" some constant or is that inteded to reflect the common notation and call the curve "C"?
2) Is your field "Conservative"? That's important.
3) Who told you that the origin is different from any of its neighbors? Defined there, with a conservative field, I don't understand that idea.

 

[bugatti79]

1) It's not perfectly clear to me what your curve is. Is "c" some constant or is that inteded to reflect the common notation and call the curve "C"?
2) Is your field "Conservative"? That's important.
3) Who told you that the origin is different from any of its neighbors? Defined there, with a conservative field, I don't understand that idea.

1) Yes I meant capital C

2) I thought the check for conservative was a check for vector fields. Is the above not a vector field, ie there is no i j k etc

3) Thats my interpretation, can you explain?

Thanks

 

[tkhunny]

1) Well, then I am even more puzzled. If you are using "C" simply to suggest the name of your path, you have not suggested much.
2) You can imagine i and j, even though this has not been specifically stated.
3) Simple, closed path in a conservative field. You should get zero (0).

 

[bugatti79]

1) Well, then I am even more puzzled. If you are using "C" simply to suggest the name of your path, you have not suggested much.
2) You can imagine i and j, even though this has not been specifically stated.
3) Simple, closed path in a conservative field. You should get zero (0).

1) That is what is given in the worksheet. So I guess it was a simple question..

3) Well in my notes it states 2 cases a) When C does not enclose (0,0), then the evaluation =0 and b) When C does enclose (0,0), it is non zero.

Now in this case we are given C as the ellipse which I understand to be at the centre at 0, so I thought the answer must be non zero...?

What do I not understand?

Thanks.