Answer:
From Green's theorem, the circulation of a function F(x,y) around a circle is given as
∫(F(x,y).dA = Area of the circle
π(3^2) - π(0^2) = 9π
Since the result is oriented counter-clockwise, the result will take negative value.
The circulation of F(x,y) is -9π
Step-by-step explanation:
∫c (4y dx + 2xy dy)
= ∫∫ [(∂/∂x)(2xy) - (∂/∂y)(4y)] dA, by Green's Theorem
By integrating the function F(x,y) = 4yi + 2xyj, around the circle, the result is πr2[3, 0], from origin 0, to radius of 3
