Objectives
- Explain the definition and interpretation of a line integral of a vector field
- Explore physical applications and visual approximations of these line integrals
Section 9.2 Line Integrals of Vector Fields
In this lesson, the line integral of a vector field is defined and motivated by measuring the amount of a vector field that lines in the same direction as a curve in space. The vector line integral is further motivated by the common physical application of calculating the work done by a vector field. The vector line integral can be visualized as a scalar line integral where the scalar function is the dot product of the vector field and the unit tangent vectors of the curve. Further, this analogy is animated for several examples where the user can assess whether the resulting line integral will be positive, negative, or zero.
