Let F(x,y)=<<xy^2+8x, x^2y-8y>>. Compute the flux oint F * nds of F across a simple closed curve that is the boundary of the half-disk given by x^2+y^2<=7, y>= 0 using the vector form Green's Theorem. oint F * nds = ?

Ramsey 2020-12-17 Answered
Let F(x,y)=xy2+8x,x2y8y. Compute the flux Fnds of F across a simple closed curve that is the boundary of the half-disk given by x2+y27,y0 using the vector form Greens
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Expert Answer

Clara Reese
Answered 2020-12-18 Author has 120 answers
Step 1
Consider the equation
Step 2
F(x,y)=(xy2+8x,x2y8y)
F.nds==×DdA
F.nds=S(8xdy+y)=3π
(8x,y).(x,y)ds=8xdy+y(dx)
x=cos0y=sin0ds=rd0ds=d0 because the radius is 1
dx=yd0dy=cos0d0
(y,8x).dx
SNxMy=3
(the area) =3(π(1)2)=3π
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