# Question #36742

##### 1 Answer

#### Answer:

See below

#### Explanation:

The work done in a conservative force field is guaranteed to be zero **only** over a closed path.

By definition, a vector field is conservative if and only if there exists a potential function

For a force field, we have the definition of work as:

....where

The **Gradient Theorem** , aka the Fudamental Theorem for Line Integrals, states that:

This is where the idea of path independence comes from.

Now, if