Answer
Figure 2 (A): the line integral appears to have positive value.
Figure 2 (B): the line integral appears to have zero value.
Figure 2 (C): the line integral appears to have zero value.
Figure 2 (D): the line integral appears to have negative value.
So,
1. the line integrals in Figure 2 (B) and Figure 2 (C) appear to have zero value.
2. the line integral in Figure 2 (D) appears to have negative value.
Work Step by Step
Figure 2 (A):
The vector directions of ${\bf{F}}$ on the upper half are in the same directions as the orientation of the path. However, on the lower half some of ${\bf{F}}$ are in reverse directions to the path and some perpendicular to it. The upper half line integral is more positive than the lower half ones, so the line integral of the closed path appears to have a positive value.
Figure 2 (B):
The vector directions of ${\bf{F}}$ are mostly perpendicular to the path. While at the left and right hand sides, the direction differs, so we expect the line integrals cancels out there. In total, the line integral of the closed path appears to have a value of zero.
Figure 2 (C):
The vector directions of ${\bf{F}}$ are perpendicular to the path, so the line integral of the closed path appears to have a value of zero.
Figure 2 (D):
Here, the vector directions of ${\bf{F}}$ are in reverse directions to the path, so the line integral of the closed path appears to have a negative value.
