# Line Integral

1. Nov 18, 2014

### ewr

In the problem attached, why is the integral become just the length of line cf?

Last edited: Nov 18, 2014
2. Nov 18, 2014

### Staff: Mentor

That result pretty much follows from the definition of a line integral. If you're not familiar with that concept, google will find you some pretty decent explanations.

3. Nov 18, 2014

### Staff: Mentor

Note that in part (a) the integral becomes just the length of line if, that is, d.
$$V_f - V_i = -\int^f_i {\vec E \cdot d\vec s} = -\int^f_i {E(\cos 0^\circ)ds} = -E \int^f_i {ds} = -Ed$$