# Vector Line Integral

1 min read

**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 = x^{3}. 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 = t^{2}, z = t^{3}

**Solution:** We have

∴ t varies from 0 to 1.