# Apply Green’s theorem to find the outward flux for the field F(x,y)=tan^(−1)(y/x)i+ln(x^2+y^2)j

Apply Green’s theorem to find the outward flux for the field
$F\left(x,y\right)={\mathrm{tan}}^{-1}\left(\frac{y}{x}\right)i+\mathrm{ln}\left({x}^{2}+{y}^{2}\right)j$
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Step 1
We are given that $F\left(x,y\right)={\mathrm{tan}}^{-1}\left(\frac{y}{x}\right)i+\mathrm{ln}\left({x}^{2}+{y}^{2}\right)j$ and the curve C defined as the boundary of the given region.
We will be using Greens