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Line integrals in vector fields
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.
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
Understanding how to parametrize a reverse path for the same curve.
Showing that the line integral of a scalar field is independent of path direction
Showing that, unlike line integrals of scalar fields, line integrals over vector fields are path direction dependent
Showing that if a vector field is the gradient of a scalar field, then its line integral is path independent
Showing that the line integral along closed curves of conservative vector fields is zero
Example of taking a closed line integral of a conservative field
Using path independence of a conservative vector field to solve a line integral