to be in the negative sense if the direction of integration is clockwise.
The sense of integration is the same as that for angular measure. The
situation is illustrated in figure 6-20.
Figure 6-20. Direction of integration for line integrals.
The direction of integration around a simple closed curve can be
referenced with respect to the unit outward normal eˆn and to the unit
tangent vector ˆet to the simple close curve as the direction of the unit
tangent produces an oriented simple closed curve.
6. If the direction of integration is reversed, then the sign of the line integral
changes so that one can write
...............................................................
∫
..............................
C
F·dr =−...............................................................
∫
............................
C
F·dr
Example 6-31. Consider a particle moving in a two-dimensional force field,
where at any point (x, y )the force in pounds acting on the particle is given by
F=F(x, y ) = (x^2 +y)ˆe 1 +xy eˆ 2
Find the work done in moving the particle from the origin to the point Balong the
path illustrated in figure 6-21, where distance traveled is measured in units of feet.
Solution: Let r =xˆe 1 +yeˆ 2 denote the position vector of a point on the path OAB
illustrated in figure 21. The work done is obtained by evaluating the line integral
W=
∫B
0
F·dr
