# Definitions > [!NOTE] Definition > Let $\underline{F}:U\subset \mathbb{R}^{n}\to \mathbb{R}^{n}$ be a [[Vector Field on Subset of Real n-Space|vector field]]. Let $C\subset U$ be a [[Parametrized Curve|curve parametrized]] by $\underline{r}:I\subset \mathbb{R}\to \mathbb{R}^{n}.$ Then line integral of $\underline{F}$ along $C$ is the [[Riemann integration|integral]] $\int_{C} \underline{F} \cdot \, d\underline{r} = \int \underline{F} \cdot \frac{d\underline{r}}{dt} \, dt $where $\cdot$ is the [[Dot Product in Real n-Space|dot product]]. **Notation**: a line integral around a closed curve $C$ is denoted $\oint_{C} \underline{F} d\underline{r}.$ # Properties #todo Since $\underline{r}'(t)$ is the tangent vector along $C$, the line integral quantifies the ?tendency? of the vector field $\underline{F}$ to point in the same direction as $C$.