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Math Help - Green's Theorem - help please

  1. #1
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    Question 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.
    =========================================
    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.
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  2. #2
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    Quote Originally Posted by kittycat View Post
    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.
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