Calculus 3: Line integrals

Apply the fundamental theorem of line integrals to measure the flow along a curve when the vector field can be written as the gradient of a function.

Compute the line integral of the vector field F on a curve $C$, using the parameterization $\mathbf{r}(t)$ from $t = a$ to $t = b$. The line integral is given by $\int_{a}^{b} \mathbf{F}(\mathbf{r}(t)) \cdot \frac{d\mathbf{r}}{dt} \, dt$.