Vector Line Integral

Vector Line Integral:

If is the force acting on a particle at a point P whose positive vector is r on a curve C then represent physically the total work done in moving the particle along C.

Thus total work done is;

Example On Vector Line Integral:

1. IF Evaluate along the curve y = x³. in the xy-plane from (1,1) to (2,8).

Solution: We have

2. IF Evaluate from (0,0,0) and (1,1,1) along the path x= t, y = t², z = t³

Solution: We have

∴ t varies from 0 to 1.