# Line integrals in vector fields

9 videos

You've done some work with line integral with scalar functions and you know something about parameterizing position-vector valued functions. In that case, welcome! You are now ready to explore a core tool math and physics: the line integral for vector fields. Need to know the work done as a mass is moved through a gravitational field. No sweat with line integrals.

### Line integrals and vector fields

VIDEO
16:46 minutes

Using line integrals to find the work done on a particle moving through a vector field

### Using a line integral to find the work done by a vector field example

VIDEO
11:32 minutes

Using a line integral to find the work done by a vector field example

### Parametrization of a reverse path

VIDEO
7:26 minutes

Understanding how to parametrize a reverse path for the same curve.

### Scalar field line integral independent of path direction

VIDEO
16:22 minutes

Showing that the line integral of a scalar field is independent of path direction

### Vector field line integrals dependent on path direction

VIDEO
15:51 minutes

Showing that, unlike line integrals of scalar fields, line integrals over vector fields are path direction dependent

### Path independence for line integrals

VIDEO
17:14 minutes

Showing that if a vector field is the gradient of a scalar field, then its line integral is path independent

### Closed curve line integrals of conservative vector fields

VIDEO
8:25 minutes

Showing that the line integral along closed curves of conservative vector fields is zero

### Example of closed line integral of conservative field

VIDEO
11:02 minutes

Example of taking a closed line integral of a conservative field

### Second example of line integral of conservative vector field

VIDEO
10:19 minutes

Using path independence of a conservative vector field to solve a line integral