What conditions must a domain D in the xy-plane satisfy to ensure that the value of the line integral + dy should depend only on the initial and terminal points of the path C that lies in D?
A) D must be simply connected and not contain the point (1, -1).
B) D must be connected and not contain the point (1, -1).
C) D must not contain the point (1, -1).
D) D must be simply connected and must contain the point (1, -1).
E) D can be any domain in the xy-plane.

Question

What conditions must a domain D in the xy-plane satisfy to ensure that the value of the line integral  +  dy should depend only on the initial and terminal points of the path C that lies in D?
A) D must be simply connected and not contain the point (1, -1). 
B) D must be connected and not contain the point (1, -1). 
C) D must not contain the point (1, -1). 
D) D must be simply connected and must contain the point (1, -1). 
E) D can be any domain in the xy-plane.

Quizplus · Accepted Answer

The Answer of What conditions must a domain D in the xy-plane satisfy to ensure that the value of the line integral  +  dy should depend only on the initial and terminal points of the path C that lies in D?
A) D must be simply connected and not contain the point (1, -1). 
B) D must be connected and not contain the point (1, -1). 
C) D must not contain the point (1, -1). 
D) D must be simply connected and must contain the point (1, -1). 
E) D can be any domain in the xy-plane.

What Conditions Must a Domain D in the Xy-Plane Satisfy