1.
Can you think of any other physical quantities that could be expressed as a line integral over either 2D or 3D curves beyond those I've introduce already?
Section 1.4 Line Integrals in 3D
Previously we looked at 2D curves, and then a function \(f(x,y)\) above that curve. However, the curve could be 3D (or more). We lose the nice geometric interpretation that we can plot in 3 dimensions (The graph of a function \(f(x,y,z)\) over a 3D curve is four dimensional). But there are lots of important physical interpretations of line integrals over 3D curves nevertheless.
Learning Objectives:
- Interpret line integrals in 3D physically (Ex: mass of wires, volumes of pipes, and arclength)
