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Math Help - Theorem of Green

  1. #1
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    Theorem of Green

    C is the segment of straight the point (a,b) to point (c,d). Calculate

    \int_C -ydx + xdy


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  2. #2
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    Quote Originally Posted by Apprentice123 View Post
    C is the segment of straight the point (a,b) to point (c,d). Calculate

    \int_C -ydx + xdy


    Green's Theorem states that

    \int_C{(L\,dx + M\,dy)} = \int{\int_D{\left(\frac{\partial M}{\partial x} - \frac{\partial L}{\partial y}\right)}}

    Where C is a positively oriented, piecewise smooth, simple closed curve in the plane, and D is the region bounded by C.


    Here L = -y, M = x so \frac{\partial L}{\partial y} = -1, \frac{\partial M}{\partial x} = 1.

    But what is your region? All you've given is a straight line. What bounds the region D?
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  3. #3
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    Quote Originally Posted by Prove It View Post
    Green's Theorem states that

    \int_C{(L\,dx + M\,dy)} = \int{\int_D{\left(\frac{\partial M}{\partial x} - \frac{\partial L}{\partial y}\right)}}

    Where C is a positively oriented, piecewise smooth, simple closed curve in the plane, and D is the region bounded by C.


    Here L = -y, M = x so \frac{\partial L}{\partial y} = -1, \frac{\partial M}{\partial x} = 1.

    But what is your region? All you've given is a straight line. What bounds the region D?
    I thinks all he wants is the line integral along the straight line from (a,b) to (c,d).
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  4. #4
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    Quote Originally Posted by danny arrigo View Post
    I thinks all he wants is the line integral along the straight line from (a,b) to (c,d).
    The answer is
    ad - bc
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