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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