Green’s Theorem, flux form Consider the following regions R and vector fields F. a. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in Green’s Theorem and check for consistency. F = <<x, y>>, R = {(x, y): x^2 + y^2 <= 4}

geduiwelh 2020-12-02 Answered
Green’s Theorem, flux form Consider the following regions R and vector fields F.
a. Compute the two-dimensional divergence of the vector field.
b. Evaluate both integrals in Green’s Theorem and check for consistency.
F=x,y,R={(x,y):x2+y24}
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Expert Answer

Faiza Fuller
Answered 2020-12-03 Author has 108 answers
Step 1
a.
To compute the divergence of the vector field F.
Given F(x,y)=xi+yj.
The divergence of F is ÷F=dfdx+dgdy.
Here f(x,y)=x and g(x,y)=y.
÷F=dfdx+dgdy
=1+1
=0
Thus the two dimensional divergence of the vector field is 2.
Step 2
b.
To evaluate the integrals of Greens Theorem:
By Greens theorem cfdx+gdy=R(dgdxdfdy)dA.
R(dgdxdfdy)dA=R(00)dA
=0
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