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The theorem statement is the following. Let ''C'' be a positively oriented, Piecewise Smooth , Simple Closed Curve in the plane and let ''D'' be the region bounded by ''C''. If ''L'' and ''M'' have continuous Partial Derivatives on an open region containing ''D'', then : Sometimes a small circle is placed on top of the integral symbol: : This indicates that the curve ''C'' is closed. To indicate positive orientation, an arrow pointing in the counter-clockwise direction is sometimes drawn in the circle over the integral symbol. PROOF OF GREEN'S THEOREM WHEN ''D'' IS A SIMPLE REGION If it can be shown that : and : are true, then Green's theorem is proven. We define a region ''D'' that is simple enough for our purposes. If region ''D'' is expressed such that: |
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