Find the value of the line integral on the closed path consisting of line segments from to from to and then from to where . (Hint: If F is conservative, the integration may be easier on an alternate path.)
A) 99
B) 12
C) 36
D) 30
E) 0

Question

Find the value of the line integral  on the closed path consisting of line segments from  to  from  to  and then from  to  where  . (Hint: If F is conservative, the integration may be easier on an alternate path.)
A) 99 
B) 12 
C) 36 
D) 30 
E) 0

Quizplus · Accepted Answer

Since the problem does not provide any information about the vector field, we cannot determine if the line integral is path-independent (i.e. conservative) or not. Therefore, we must evaluate the line integral directly using the given path. However, note that the starting and ending points of the path are the same, which means that the path is a closed loop. If the vector field is conservative, then the line integral over a closed loop is always zero. Hence, without any information about the vector field or any clues to suggest that it might be conservative, we can only conclude that the line integral is zero. Therefore, the answer is E.

Find the Value of the Line Integral on the Closed