Green's Theorem in the Plane
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Applications of Green's Theorem
Area of a plane region It is possible to express the area of a region R as a line integral over its boundary. In [Equation goes here - download the original pdf to see it.] let [Equation goes here - download the original pdf to see it.] then [Equation goes here - download the original pdf to see it.] , whence [Equation goes here - download the original pdf to see it.] Now [Equation goes here - download the original pdf to see it.] is the area, A, of the region R; furthermore, by putting [Equation] we obtain by a similar process [Equation goes here - download the original pdf to see it.] Adding the two results together [Equation goes here - download the original pdf to see it.] [Example goes here - download the original pdf to see it.] Area of a plane region in polar coordinates Let [Equation goes here - download the original pdf to see it.] be polar coordinates; then [Equation goes here - download the original pdf to see it.] Substitution into [Equation goes here - download the original pdf to see it.] gives [Equation goes here - download the original pdf to see it.] [Example goes here - download the original pdf to see it.]
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Contents of
Green's Theorem in the Plane
1 Green's theorem in the plane
2 Applications of Green's Theorem
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