Showing a vector field is irrational on

[tamintl]

Homework Statement

Let F = ( -y/(x²+y²) , x/(x²+y²) ) Show that this vector field is irrotational on ℝ² - {0}, the real plane less the origin. Then calculate directly the line integral of F around a circle of radius 1.

Homework Equations

The Attempt at a Solution

To show F is irrotational we must show curl v = 0. Although I'm unsure what it means by finding it on ℝ² - {0} ?

 

[Dick]

It just means find the curl at a general point (x,y) where x and y aren't both 0. The vector field is undefined at (0,0).

 

[tamintl]

okay thanks.. I got it