Editing Green's theorem (section)

==Theorem==
Let {{mvar|C}} be a positively [[Curve orientation|oriented]], [[piecewise]] [[Smoothness|smooth]], [[simple closed curve]] in a [[plane (mathematics)|plane]], and let {{mvar|D}} be the region bounded by {{mvar|C}}. If {{mvar|L}} and {{mvar|M}} are functions of {{math|(''x'', ''y'')}} defined on an [[Open set|open region]] containing {{mvar|D}} and have [[Continuous function|continuous]] [[partial derivatives]] there, then

<math display="block">\oint_C (L\, dx + M\, dy) = \iint_{D} \left(\frac{\partial M}{\partial x} - \frac{\partial L}{\partial y}\right) dA</math>

where the path of integration along {{mvar|C}} is [[counterclockwise]].<ref>{{Cite book |last1=Riley |first1=Kenneth F. |author-link1=Ken Riley (physicist) |url=https://archive.org/details/mathematicalmeth00rile |title=Mathematical methods for physics and engineering |last2=Hobson |first2=Michael P. |last3=Bence |first3=Stephen J. |publisher=[[Cambridge University Press]] |year=2010 |isbn=978-0-521-86153-3 |edition=3rd |location=Cambridge |url-access=registration}}</ref><ref>{{Cite book |last1=Lipschutz |first1=Seymour |author-link1=Seymour Lipschutz |url=https://books.google.com/books?id=4O4zZu_2XnMC |title=Vector analysis and an introduction to tensor analysis |last2=Spiegel |first2=Murray R. |author-link2=Murray R. Spiegel |publisher=[[McGraw Hill Education]] |year=2009 |isbn=978-0-07-161545-7 |edition=2nd |series=Schaum's outline series |location=New York |oclc=244060713}}</ref>