1. ## Green's Theorem - help please

Question 1

Use Green's theorem to evaluate the integral . Assume that the curve C is oriented counterclockwise.

the integral of c of y*tan^2 x dx + tan x dy

where c is the circle x^2 +(y+1)^2 =1.

Please show me the steps of how to solve it if possible. Thank you very much.
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question 2

Evaluate the integral

the integral of c of (-ydx+xdy)/(x^2+y^2)

if c is a positive smooth simple closed curve oriented counterclockwise such that
a) C DOES NOT ENCLOSE THE ORIGIN
b) C ENCLOSES THE ORIGIN.

um... for this question. I just don't get the picture and meaning of
a) C DOES NOT ENCLOSE THE ORIGIN
b) C ENCLOSES THE ORIGIN.

Could you please explain this to me maybe with a picture if possible ? Thank you very much.

Please don't show me how to calculate the second question because I have the solution for this question.

2. Originally Posted by kittycat
question 2

Evaluate the integral

the integral of c of (-ydx+xdy)/(x^2+y^2)

if c is a positive smooth simple closed curve oriented counterclockwise such that
a) C DOES NOT ENCLOSE THE ORIGIN
b) C ENCLOSES THE ORIGIN.

um... for this question. I just don't get the picture and meaning of
a) C DOES NOT ENCLOSE THE ORIGIN
b) C ENCLOSES THE ORIGIN.

Could you please explain this to me maybe with a picture if possible ? Thank you very much.

Please don't show me how to calculate the second question because I have the solution for this question.
This happens to be an very interesting integral. "Enclosing the origin" means the region which we are integrating over contains the origin.