Consider the line integral for the vector field given by F=(1/x)i+(1/y)j and the
ID: 2861958 • Letter: C
Question
Consider the line integral for the vector field given by F=(1/x)i+(1/y)j and the path given by the unit circle, centered at the origin, counter-clockwise. You can not use Greens Theorem on this line integral. Why?
A. The region is not simple and/or the path is not simple
B. The vector field is not Path Independent
C. The vector field is path Independent
D. Because 1/x and 1/y do not have continuous partial derivatives over the region R. since the region contains (0,0)
I'm leaning towards A or D because B,C path independence shouldn't matter. I can't tell about A because there is no picture. D sounds like the most since to me but just double checking.
Explanation / Answer
A path is simple if the curve encompassing it does not cross itself. Here the circle does not cross itself so the path is simple.
How ever, 1/x and 1/y are not defined at x=0 and y=0 and when ever the field is taken in account when the x=0 or the y=0 , this will create problem. Hence this is the right anght answer.
Path independence have no role to play here.