I'm studying line integrals of vector fields and I can't do this prove:
Let $\gamma : [a,b] \rightarrow \mathbb{R}^m$ a regular parameterized curve e $F$ a continuous vector field defined over the image of $\gamma,\: C=\gamma([a,b])$, with values in $\mathbb{R}^m$. So, the line integral of $F$ over $\gamma$ is given by the formula:
$$\int_\gamma F \cdot d\vec{r} = \int_b^a F(\gamma(t)) \cdot \gamma ' (t)dt$$
I'm trying but i can't understand this $d \vec{r}$:
Can someone help me? I would be very grateful.