Question regarding Greens theorem

[Kuma]

Homework Statement

I have some questions similar to this one. I have to just provide reasoning as to why this can or cannot be evaluated using greens theorem.

given f = x/sqrt(x^2+y^2) dx + y/sqrt(x^2+y^2) dy, and the curve c is the unit circle around the origin. Why can/cannot the integral of f around c be evaluated using greens theorem?

Homework Equations

The Attempt at a Solution

So I said that because taking P as the first term and Q as the second term of f, they both don't have continuous first order partials on c (which is a condition for greens theorem) because there are restrictions on what x and y can be (ie x^2 + y^2 > 0). I'm not sure if that is right though if someone can clarify.

 

[LCKurtz]

Homework Statement

I have some questions similar to this one. I have to just provide reasoning as to why this can or cannot be evaluated using greens theorem.

given f = x/sqrt(x^2+y^2) dx + y/sqrt(x^2+y^2) dy, and the curve c is the unit circle around the origin. Why can/cannot the integral of f around c be evaluated using greens theorem?

Homework Equations

The Attempt at a Solution

So I said that because taking P as the first term and Q as the second term of f, they both don't have continuous first order partials on c (which is a condition for greens theorem) because there are restrictions on what x and y can be (ie x^2 + y^2 > 0). I'm not sure if that is right though if someone can clarify.

That's the right idea. P and Q must have continuous partials on an open region containing C and its interior, not just on C. And the problem with the partials is at (0,0).