Exercises

01

Vector line integral over a curve

Compute the line integral ${\int }_{\mathcal{C}}\mathbf{F}\cdot d\mathbf{s}$, where $\mathbf{F}=(x+y^2,xz,y+z)$ and $\mathcal{C}$ is traversed by the parametric curve $\mathbf{r}(t)=(t^2,t^3,-2t)$, $t\in [0,2]$.

02

Vector line integral over a segment

Compute the line integral ${\int }_{\mathcal{C}}\frac{-ydx+xdy}{x^2+y^2}$, where $\mathcal{C}$ is the line segment from $(1,0)$ to $(0,1)$.