If F(x,y)=<M(x,y),N(x,y)> is a vector field on the plane?

[sarahkelly]

its components M(x,y) and N(x,y) are differentiable functions that satisfy (∂N(x,y)/∂x) – (∂M(x,y)/∂y) = 1-x.

a. is it possible for the vector field to be conservative? Explain.


b. Let C be x^2+y^2=1 centered at the origin traced counter clockwise. compute the integral ∫F.dr



Since, the partial derivatives don't equal each other, they're not conservative. But how should I go about calculating this line integral?

 

[Vorde]

Well, first before we help you, you should say what you've gotten so far. Though based off the information given, I'll guess you know about Green's Theorem, in which case this is a fairly easy problem.

 

[HallsofIvy]

its components M(x,y) and N(x,y) are differentiable functions that satisfy (∂N(x,y)/∂x) – (∂M(x,y)/∂y) = 1-x.

a. is it possible for the vector field to be conservative? Explain.b. Let C be x^2+y^2=1 centered at the origin traced counter clockwise. compute the integral ∫F.dr
Since, the partial derivatives don't equal each other, they're not conservative. But how should I go about calculating this line integral?

You are not give F but you are given (∂N(x,y)/∂x) – (∂M(x,y)/∂y) = 1-x. Use Green's theorem.