Objectives
- Explore the definition of the line integral of a scalar function.
- To understand the relationship between line integrals and the one dimensional integrals from single variable calculus.
Section 9.1 Line Integrals of Scalar Functions
In this lesson, the line integral of a scalar function is defined and motived by measuring the accumulation of a scalar function along curved paths in space. The scalar line integral is visualized as a surface above the curve whose height is given by the value of the scalar function at each point on the curve. Geometrically, the conversion from the scalar line integral to a one dimensional integral on the cartesian plane is developed by using a parameterization of the curve to flatten the surface in space. This flattening is animated for several different examples where the user is asked to assess the sign of the resulting scalar line integral.
