Also recall that the “divergence
form” of Green’s theorem is
∫ F . n ds =
∫ ∫ div F
dA
C R
where R is a region in the x-y
plane enclosed by a piecewise-smooth, positively
oriented (keep region to your left as you travel around the simple
closed curve C)
F(x,y) is a vector
field F = P(x,y) i +
Q(x,y) j,
n(x,y) is a unit vector to the curve C
ds = arc
length along curve C
div F = ∂P/∂x +
∂Q/∂y
dA = element of area in R
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