[Steps Shown] Use Green's Theorem to find the integral of the vector field F(x,y)=(y+3x)\veci+(2y-x)\vecj counterclockwise around the ellipse x^2+2 y^2=1. Hint:
Question: Use Green's Theorem to find the integral of the vector field \(\vec{F}(x,y)=(y+3x)\vec{i}+(2y-x)\vec{j}\) counterclockwise around the ellipse \(x^{2}+2 y^{2}=1\). Hint: The area of the ellipse with equation \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) is \(\pi a b\).
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