Line Integrals

An integral on a curve through a multidimensional function

Requirements

1. $f$ is continuous
2. $C$ is smooth
3. $\vec{r}(t)$ is a simple parameterization of $C$, $a\le t\le b$

Solving

$${\int }_{C}f(x,y,z)ds={\int }_a^{b}f(x(t),y(t),z(t))\Vert {\vec{r}}^{\prime }(t)\Vert dt$$